If "the Kingdom of God comes not with observation", how can it be "taken by violence"? Matthew 11:12 (KJV):


  And from the days of John the Baptist until now the kingdom of heaven suffereth violence, and the violent take it by force.


Similarly, in Luke 16:16:


  The law and the prophets were until John: since that time the kingdom of God is preached, and every man presseth into it.


Whereas Luke 17:20 reads:  


  And when he was demanded of the Pharisees, when the kingdom of God should come, he answered them and said, The kingdom of God cometh not with observation: 


How can it be 'taken' as Matthew 11/Luke 16 suggests in light of what Luke 17:20 says?
The verses cited, when taken in the broader context of the pericopes to which they belong, both emphasize the importance of believers taking an active role in preparing themselves for the Kingdom of Heaven.

What Matthew reports Jesus to say in 11:12 relates to what He had just said to the multitude:


  Matthew 11:11
  
  
    Verily I say unto you, among them that are born of women, there has not arisen a greater than John the Baptist.  Notwithstanding, He that
    is less, in the kingdom of Heaven is greater than he.
  


The eastern Church Fathers (e.g. John Chrysostom, 4th century) understood Christ to be referring to Himself in Matthew 11:11.  He, Christ, was not born of woman - i.e. a married woman, gyne in Greek - but of a virgin (parthenos).  He, Christ, is "less" than John the Baptist in years (the Greek microteros also means "younger"), but He is greater in the Kingdom in Heaven.  The Kingdom of Heaven suffering violence and the violent taking it by force refers to what His followers must do to attain the Kingdom of Heaven:  leave one's father and mother (Matthew 19:29, Mark 10:29, Luke 18:29); despise one's own life (John 12:25); etc.  (See Chrysostom's Homily XXXVII on Matthew).

Similarly, I think we must consider Luke 17:20 in the context of the verse that follows:


  Luke 17:20–21 (KJV 1900)
  
  
    And when he was demanded of the Pharisees, when the kingdom of God should come, he answered them and said, The kingdom of God cometh not
    with observation: Neither shall they say, Lo here! or, lo there! for,
    behold, the kingdom of God is within you.
  


Here He is admonishing the Pharisees not to sit passively and wait for the Kingdom to come, but rather to attend to themselves in order to prepare to receive it.  Cyril of Alexandria (4th/5th c.) comments on this passage:


  For ask not, He says, about the times in which the season of the
  kingdom of heaven shall again arise and come, but rather be in
  earnest, that ye may be found worthy of it, for it is within you, that
  is, it depends on your own wills, and is in your power whether or not
  you receive it.  For every man who has attained to justification by
  means of faith in Christ, and is adorned by all virtues, is counted
  worth of the kingdom of heaven.
  
  Commentary Upon the Gospel of St. Luke, Part II, Sermon CXVII (translated from the Syriac by R. Payne Smith, Oxford University
  Press, 1859), pp. 541-542.


The Greek phrase translated as "is taken by violence" in the King James Version is βιαζεται (biazetai), a passive form of the verb βιάζω (biazo).  In the Greek, Matthew 11:12 and Luke 16:16 use the same word, βιάζω, conjugated differently.   It conveys the meaning of achieving something by force.  Both the KJV and RSV (the versions coincidentally recommended within the Greek Orthodox Church) use the word "violence" in their translations, but other versions choose something more mild.  The the NIV, NASB, and ESV omit translating the phrase βιαζεται altogether, even though it appears in all available Greek manuscripts.  Although the image of the Kingdom of Heaven being "taken by violence" may seem somewhat incongruent, the Lord Himself said that He came not to bring peace, but a sword (Matthew 10:34).  The Russian Orthodox monk and writer Theophan the Recluse provided the following exegesis of Matthew 11:12, which, although written for Russian faithful living in the late 19th century could perhaps also be applied today:


  The Kingdom suffereth violence - that is, it is attained with
  violence, with labor, force, and difficult spiritual struggles. 
  Therefore, only those who lead a labor-filled ascetic life attain it. 
  Thus, every sort of comfort is renounced along the path to the
  Kingdom.  Pleasures of all types distance us from the Kingdom.  But
  these days we have concern only for pleasures - sometimes emotional,
  but more often fleshly: to eat, drink, have fun, make merry, and
  luxuriate in everything.  We have said to the Kingdom, "I beg you to
  excuse me," although there is a feast in the Kingdom - a royal feast -
  one so sumptuous that we could not even conceive of it, because we do
  not have the taste for it.  What is considered sweet there is bitter
  to us, what is pleasant there is repulsive to us, what gladdens one
  there is a burden to us.  We have gone totally separate ways.  And the
  Kingdom, together with the violent who take it by force, withdraws
  from us.  We are glad about this, and are even ready to drive them
  away more quickly.  Indeed, we have already started talking about it,
  but the evil one has not yet managed to arrange this*.
  
  Thoughts for Every Day, p. 133


* Theophan, writing in 1881, may have been referring to the revolutionary movements - all intensely secular - that were starting to take hold in Russia at the time.  The editors note, "He identified the spiritual sickness of the modern West, with its symptoms of materialism, naturalism, deism, atheism, neopaganism, hedonism, and other antichristian belief systems."