Jesus is going to teach something important to his disciples and he will use the fact that he had just ‘overcome’ a demon (i.e. in casting the demon out of a person, thus 'dispersing' the demon from the person ) to illustrate his teaching. For the kind of people who are disciples (and/or people who might become disciples) Jesus' teaching goes far beyond just ‘demons' and 'spirits’.
     ‘To divide’ here in the Greek means to disperse away from one, and/or to hand over to others. ‘Armed’ and ‘armor’ are things that can also be money, finances, stocks and bonds, etc.; in that, these are things or tools which we use to ‘keep’ (i.e. hold on to) our homes and our goods ‘in peace' ...'wherein' we 'trust' them for our wellbeing.
    It is interesting that in teaching Jesus used the casting out of a demon essentially to illustrate his obvious strength to 'disperse' or 'to remove'. Yet, most Christians today find the passage interesting for “learning more about demons and spirits and how to war against them”.
    So for a moment, if you will, please forget about “demons and spirits”…because Jesus quickly moves on from the example of him being 'stronger' than the demon, so that he can speak straight to those who might be interested in 'discipleship' more than in ‘seeing a heavenly sign’.

     Jesus is speaking to various kinds of people in the crowd. The disciples are listening. The people crowded around Jesus (in varied modes of listening) are listening. There are 1) those ‘wondering’, 2) those condemning, and 3) those believing, but yet ‘seeking a heavenly sign’.
    May I suggest that this encompasses all of mankind through the ages that 'gathers' around Jesus. This excludes the great many people (including Christians) that could not care less one way or the other ...like the many Israelites who were passing by and not bothering to join the large crowd 'gathered' around Jesus. These latter folks realized that the famed Jesus was speaking and that some people had the time to linger and to listen and to argue intellectually; but they must be about their own business.
     Jesus continues to make this passage about himself…but also about those who would have something to do with him (i.e. for or against, good or bad). The disciples are ‘with’ Jesus. The ‘wonderers’ have not yet made up their minds about Jesus. And those ‘seeking a sign from heaven’ believe that Jesus is from heaven...... ah, but are these ‘with’ Jesus... in the sense of his concern in this passage for them to become like his disciples? (A few verses later we shall see a woman 'testifying' in behalf of Jesus.)
     Furthermore, these latter believers seem ‘strong’ in their belief that Jesus is of heaven…... so much so that they know he can perform a sign from heaven… and that he ought to do it because they are asking him… and that… well, after all, they want to be part of Jesus proving himself to the condemners… thus their ‘tempting’ request… almost in chorus from all the believers present… that he perform a heavenly sign for all to see... even for the folks passing by.

     At this point I will again consider 21-22 regarding myself and how God used this passage with me:
    I was a ‘strong man’ ‘armed’ with my Masters Degree in electrical and ocean engineering... and with a good paying job, and with my abilities, and with the several houses that we owned and rented, etc.
    Ah, but (the Lord having first conquered my willingness) I was ‘overcome’ by the very Jesus who is speaking to the people in this passage. In very fact, Jesus 'dispersed' my ‘amour in which I trusted’. All along I had loved the Lord God and His Son dearly. During our first five years in Wyoming, the ‘spoils' of our saving 'diminished' to nothing.
    In other words, when all was sold in Florida and we moved to Wyoming, we offered all of it to him for His purpose in us. Yes, we would be glad to live on His provision which we expected to be in some kind of ministry. However, the ‘spoils’ (our savings which had been given to God and owned by Him) ... all of which we expected Him to use in our new life for Him ... well, these were used up in five years while we “waited upon the Lord”. It was only then that He begin providing for us in His manner as He chose to do ... and He still does.
    God did not take from us our 'spoils', instead He caused us to live-away our 'spoils' until they were gone. Understand: all of our 'spoils' before moving to Wyoming had been blessings from God even as He provided both of us with jobs, a blessed son, ownership of houses, etc. Then, as the 'spoils' were near disappearing, He began to deal with us (in a way different than before) about faith, which was in us and often used by Him. But now He was going to be using our faith in ways yet experienced by us. God has different methods of provision for His different purposes.

     Wealth gotten by vanity [for this illustration 'by my own self-worth'] shall be diminished: but he that gathereth by labour [i.e. by the hand, in this case 'by God's Hand'] shall increase. Hope deferred maketh the heart sick: but when the desire [of the thing hoped for] cometh, it is a tree of life. Whoso despiseth [i.e. counts of little value] the word [of God's personal instruction for him] shall be destroyed: but he that feareth the commandment [which God has for him] shall be rewarded.
Proverbs 13:11-13

     It is interesting (to Barbara and to me) how God might ignore what a person has done in his or her own strength (even if the thing done was done with God’s helping hand) ...... and then He turns unexpectedly to doing new and different things for the person that has surrendered to Him enough for Him to change course. Actually one finds out later that it was all in the plan.
     Ah, and God may repeat the change-process when He begins another new thing. Indeed, He may allow, or cause to be ‘dispersed’, the very thing or money which the surrendered-one thought was being provided for some new thing (as with us and our savings).
    This usually works to focus the surrendered-one upon God instead of being focused upon incoming provisions and their probable usage. In other words, stop looking at what you can see and instead focus upon your unseen God. Indeed, 'wonder' all you want, as it is natural to one who is captured (i.e. imprisoned) by a Holy God.
    The new something may be separate from past somethings... and the past somethings may have very little if anything to do with the new thing of the future.
     Yes, it can be confusing; but not so much if the surrendered-one is fully dependent on his King.
    Yet, as a new thing is unfolding it can really be a great relief in seeing old things being ‘dispersed’ (i.e. as water spilled and seeping into the ground). In fact, you may have been working hard to protect a particular provision which continues spilling. However, when it is gone, then also is gone the striving to protect it. The lack of such striving (for God's purpose you may think) may provide significant relief and a new opportunity to gaze (as a little child) toward the Father... not so much for answers, but just to gaze.

     Verses 21-22 are about Jesus referring to himself as the ‘stronger’ of two strong ones, and this is why and how he cast out the ‘strong’ demon. Then verse 23 makes it clear (regarding Jesus and his work) that there are only two positions: ‘with him’ working, or ‘against him’ working. That is, if a Christian is in the vicinity of Jesus working his work, then he or she should either leave the vicinity or become guilty of one of these two positions.
     Jesus now returns to the example of casting out the demon. He is not so interested in teaching about 'unclean spirits' as much as he is interested in teaching about how a person... cleaned up inside... can fall back into a state worse than his initial state. That is, if the Christian does not fill the cleaned space with something 'stronger' than that which was 'dispersed' from the cleaned space then something 'strong' may well return to the space. Please remember that Jesus was primarily teaching to his many disciples, the twelve disciples, and to those gathered around him who might become disciples. Real discipleship has its many dangers. However, those disciples who become captured by the Master have differing dangers, as the Twelve would come to experience. Indeed, this is why Luke is writing this passage.
     So then, now forget for a moment about 'spirits' coming and going. Become concerned with the cleaned space in you becoming filled with things ‘stronger’ regarding Jesus' purpose. This does not make the 'dispersed' (i.e. now cleaned) person stronger, but it does eliminate the earlier ‘strong’ thing from returning. So what is Jesus' purpose for a cleaned space inside you? He will not tell the potential disciple anything except, "Follow me".
    If the Christian never has had an ‘unclean spirit’ in the first place, this is very good. I have never known such a Christian. It seems that Jesus primarily died for the sick and not for well ones. (Even so, 'unclean spirits' are always looking for a home.) The one following close ‘with’ Jesus is strong only in his own weakness.
     Example: Being moved by God to renew one’s self is a cleaning experience. Ah, but the clean space is supposed to be for something ‘stronger’ than what has been 'dispersed'. Many a sincere Christian goes through many re-dedications (in younger adult years I did for a while), but then later nothing significant has occurred in him. Then the result can be a hardening toward future similar wooing by God. Indeed, God may give up wooing one who has been very sincere toward Him, due to not allowing a 'stronger' something to be installed. (This often happens due to fear of what God might do with the new something.)
    I are speaking of a child of God growing in things of the church, doctrine, service etc., yet he or she has not allowed the cleaned space in him to be filled with something 'stronger'. A 'stronger' something is not church, doctrine, knowledge, service, or any such thing "for God". These are fine and I would say "necessary". But 'stronger' points to the 'stronger' One. A 'stronger' something is something of God the Father and/or of Jesus the Son. Every night I pray, "Father, if you would, please do something in me and something in Barbara that is of you... or of Jesus... or of the Holy Ghost... or of your kingdom... or of your Word... and I fall asleep. What does He do or not do? That is His business. Even so, I oft times 'wonder'.
     The child of God cleaned, but not having the space filled with something 'stronger' that entirely fends off the 'strong' 'spirits', is still not ‘with’ Jesus (as in this whole passage). The child of God that is oft fighting to stay clean is very weary. Perhaps church becomes too challenging. (And too many evangelical churches these days are entirely too challenging to its members, challenging "to be happy in the Lord", "to get out and witness", "to be friendly to your neighbors and go over and cut their lawn"....)
    Such a child of God may well be working for God while at the same time he or she is not ‘with’ Jesus in his kind of ‘gathering’. Here Jesus was not teaching about 'demons', 'unclean spirit', and the like. It was about spaces cleaned or 'dispersed' by Jesus (like inside the man who no longer had a demon). Being cleaned by Jesus is for a Jesus-purpose, which has something to do with Jesus-gathering. Seldom do we know about the purpose or the gathering until later. For this is what Biblical faith is all about. (Read my book, God's Hook... free for downloading).

     Christians usually calculate that this verse could not possibly be about Christians because Christians do not want to think that it might be about Christians. Note that the word ‘wicked’ did not occur in this whole passage until now. Moreover, it has less to do with 'spirits' as it has to do with emptied clean spaces ‘swept and garnished’… which cleaned spaces were accomplished by Jesus’ work. In Jesus' travels... were there many really evil and wicked people from whom Jesus cast out 'demons' and 'unclean spirits'? Answer: No…only needy men and women that sought him; only those who desired to be set free by the Son of God, their Messiah. Every real Christian is a sinner... who at one time had to respond “Yes” to Jesus’ bloody sacrifice. How much more is left in you and in me for the Father and His Son to fill 'stronger' things of Themselves? 
     Dear Christian, next time God convicts you of something and wants His way with you (and pray that He does come to you for this) then allow Him to clean a space in you and allow Him to fill the space with something ‘stronger’. Yes, it is scary.

     This dear lady is one of the believers in Jesus (i.e. that he is the Son of God come from heaven and he can perform heavenly signs). She is a believer, and here is her method of working for Jesus. Her method is giving testimony, if you will, that this man is The One. She says it in front of all the people.
    She may not yet understand that he is the Messiah, but she surely knows that he is straight out of heaven. And she knows that ‘the womb [i.e. of Mary] that bare thee, and the paps which thou hast sucked’ were surely ‘blessed’.
    However, Jesus viewed her as a distraction. She was 'tempting' Jesus to acknowledge her and perhaps even bless her for her action. But Jesus continued teaching his disciples and those of the crowd who might be interested in true  discipleship.

     See Matthew 19:16-30 about the Rich Young Ruler. He came seeking the word of God, even to becoming a disciple to follow Jesus. Yet, he could not ‘keep’ the word that Jesus offered him because, while he was focused upon offering himself into discipleship (and surely offering his riches also), Jesus would have him to go sell (i.e. ‘disperse’) his riches, give to the poor, and then follow. Barbara and I did not have riches, but what we did have lasted five years (living in a trailer house, growing a garden, cutting firewood for heat, raising rabbits and goats, etc).
    At the time of this passage, even Jesus’ disciples did not comprehend why Jesus turned the Rich Young Ruler away in this manner. Surely, they use the man’s riches within Jesus’ ministry. Ah, but the Father's work had to be accomplished by the Father and His riches.
     The dear woman also was not getting it. She desired to bless Jesus with her testimony and her recognition of him, even in a crowd that had haters and condemners of Jesus that might report her to the temple leaders who might disallow her from entering the temple. Like this woman, this is the kind of thing that you, dear reader, and I might wish to do for Jesus. But note that this woman was not ‘with’ Jesus. She was, in fact, ‘scattering’… even though she did not realize it in giving testimony.
     Luke included verses 27 and 28 to illustrate how the children of God so easily miss within their own understanding ‘the word of God’. The disciples of Jesus, including the Twelve, had their hearts and inner spaces cleaned by Jesus; but they were not yet ready to be filled with the 'stronger' 'word of God'. Indeed, we (each and every one of us) miss out on the 'stronger' 'word of God’ until we are ready to receive it; in that, ‘many are called [at any given time] but few are chosen.’ I suspect that soon enough this dear woman did “get it”... perhaps when she heard the clear 'stronger' testimony and knew it to be true that Jesus had risen. Our Lord was not speaking of understanding and knowledge. He was speaking of something of God that was 'stronger'. 

     Jesus is giving another example: Two kinds of ‘light’ are mentioned (i.e. here our use of the word ‘light’ is twofold). One is the light source, which in this verse is the ‘candle…on a candlestick’. The second is the radiance of the candle’s flame, which is 'light' to see by. The purpose of a candle is to make light (i.e. radiance), and the 'light' (radiance) is for the purpose of folks seeing what there is to see. Now Jesus will apply the example.

     Think of the moon as you attempt to walk at night in the moonlight. Though the sun is the actual light source, the moon, by gathering in sunlight and reflecting it to the earth, becomes a secondary light source.
    Similarly, the ‘light of the body is the eye’ where (like the moon) the eye is the light source of the body... and it can make ‘thy whole body also is full of light’; however, the eye can only do this ‘when thine eye is single’.
     Therefore, Jesus says that the (spiritual) eye is like a lens that, when focused ‘singularly’, draws (spiritual) 'light' into itself and then passes it into the body. Indeed this kind of light can invade the ‘whole body’ for God’s good purpose in His child.
     Therefore, we now combined these two verses with the above discussed verses: The clean space can become full of this kind of ‘stronger’ 'light'…and this kind of ‘stronger’ 'light' is death to the creatures of darkness because the creatures of darkness cannot abide God's 'light' and must have darkness as their light.
     Ah, but dear reader, we know that the creatures of darkness actually can abide just a tiny bit of light which may creep into their dark dank holes. And we know that “darkness is the absence of light”. Moreover, the basic meaning of the word ‘evil’ is hurtful, And we know that an unfocused spiritual eye of a Christian is not ‘single’. Therefore, we know that the 'light' emitting here from Jesus’ teachings, which strikes our (spiritual) eye, can become defused such that only a little of the light enters a Christian's spiritual body. (Jesus is speaking of and to Christians.) Therefore, we know by Jesus’ words that there is clean space inside a Christian where things of darkness (i.e. things of the world) might dwell… which space needs to be cleaned or 'dispersed' and filled with ‘stronger’ things.

     Dear reader, we are not speaking particularly of demons and unclean spirits in Christians; instead we are speaking of a Christian’s values and heart desires that are not pure. And as such the worldly values and desires cannot abide the pure light of the word any more than can the creatures of darkness abide the pure light of the word. Therefore, should the pure light of the word be allowed to somehow enter (i.e. penetrate) the Christian’s inner man, then the values and desires that are not pure must leave… that is, if the Christian holds on to the newly entered pure light of the word... that is, if the Christian is allowing his or her inner man to be 'dispersed'.
    Jesus is not condemning or putting down Christians (like the woman who blessed Jesus) whom he has cleaned in their faith in him. He is speaking to the fewer Christians who (like the Rich Young Ruler) really want to follow him is the manner of absolute discipleship. He is telling of what lies ahead for them if they remain 'gathered' to him.
    (Yet, thank you Father that you sent your Son to die for the world... and you have so many good things for those who have accepted your Son and are now your children.)
     Are we not sinners, though saved? Is there not a place in each of us where God wishes to 'disperse'? Is it not true that the pure 'light' is the ‘gathering kind of 'light'’? Is it not true that diffused light, diffused inwardly by the Christian's eye not being 'single' results in the pure 'light of the word' becoming ‘scattered’ inside the Christian? Is there not many many differing concepts, doctrines, church-purposes, etc. among all the brethren? Was it not so in the Bible both Old and New Testament ages among God's people?
     Therefore, we know that a single eye that passes though the focused pure 'light' will enlighten the whole spiritual body. Such light is the word of God when it enters and is 'kept'. This condition makes for a blessed condition, as one lives and walks in faith before a pleased Heavenly Father (Hebrews 11:6). It is the condition which allows a person to be ‘with’ Jesus’ whenever and wherever he might be ‘gathering’.