How would the four major eschatological views differ in their interpretation of Revelation 21:4? Under "Christian eschatology," Wikipedia lists four contrasting beliefs pertaining to apocalyptic literature (and prophecy?) in the Bible:


Preterism
Idealism
Historicism
Futurism


How would each of these camps interpret the following prediction, which comes on the heels of the "new heaven and new earth," the "new Jerusalem, coming down out of heaven from God," and a promise that God "will dwell among them":


  He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away. -Revelation 21:4


What does this mean, and when did/will it happen? Please include a source to a teaching from each perspective on this verse if possible.
I really like this question because it is reasonable to ask and it phrased in a way that indicates it is a real question. First of all, the categories you listed are not applicable for Rev Chapters 1-3 and Rev 20-22. They are the categories that apply to Rev 4-20.  Secondly, Chapter 20 is split along these categories, which also do not really apply but may create a directional tendency just as the previous categories do: 

•   Premillennial (a literal 1000 year binding of Satan after Christ returns before the new heaven and earth of Chapter 21)

•   Postmillennial Approach (a literal or symbolic period of greatness in the church expected just prior to the Lord's return)

•   Amillennial (basically the 1000 years is from the first coming to the second coming of Christ)

Therefore as we approach Chapter 21 we basically face it with these possible 10 positions in very simplified form:


Preterism/Postmillennial 
Preterism/Amillennial 
Idealism/Postmillennial 
Idealism/Amillennial 
Historicism/Premillennial 
Historicism/Postmillennial
Historicism/Amillennial
Futurism/Premillenial/Pre-tribulation
Futurism/Premillenial/Post-tribulation 
Futurism/Premillenial/(no rapture)


Now what are we to think as we come to Chapter 21? Well, all these ten views must be multiplied into new variants as the new heavens and the new earth can be taken literally, or symbolically or combination therefore along any possible view before mentioned.  In virtually all (if not literally all) views this represents heaven after the final judgment where we live forever with Christ, but a more literal view will make that incomprehensible heavenly state a ‘heaven on a renewed physical earth’ and a more literal view might even literally say there is no ocean etc. as literally described. This means we now have these choices:


Preterism/Postmillennial/Literal Earth – Everything in Revelation happened around the siege and destruction of Jerusalem. However a great final revival (see note) in the world will occur before the final judgment. After which we will literally live with Christ on a new planet earth.
Preterism/Amillennial/Literal Earth – Everything in Revelation happened around the siege and destruction of Jerusalem. However Revelation speaks loudly to us now and at 'all times'. After the end of the world we will literally live with Christ on a new planet earth.
Preterism/Postmillennial/Symbolic Earth – Everything in Revelation happened around the siege and destruction of Jerusalem. However a great final revival in world will occur before the final judgment. After which we will literally live with Christ in heaven.
Preterism/Amillennial/Symbolic Earth – Everything in Revelation happened around the siege and destruction of Jerusalem. However Revelation speaks loudly to us now and at all times. After which we will literally live with Christ in heaven.
Idealism/Postmillennial/Literal Earth – All the symbolic scenes speak to us at all times and some indicate a great future revival. After which we will literally live with Christ on a new planet earth.
Idealism/Amillennial/Literal Earth – All the symbolic scenes speak to us at all times and this is during the 1000 years in which we live. After which we will literally live with Christ on a new planet earth.
Idealism/Postmillennial/Symbolic Earth – All the symbolic scenes speak to us at all times and some indicate a great future revival. After which we will literally live with Christ in heaven.
Idealism/Amillennial/Symbolic Earth – All the symbolic scenes speak to us at all times and this is during the 1000 years in which we live. After which we will literally live with Christ in heaven.
Historicism/Premillennial/Literal Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come and we will literally reign with him 1000 years before the new heaven and the new earth. After which we will literally live with Christ on a new planet earth.
Historicism/Postmillennial/Literal Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come and before that there will be a great revival. After which we will literally live with Christ on a new planet earth.
Historicism/Amillennial/Literal Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come but there is no need to expect a great revival before then. After which we will literally live with Christ on a new planet earth.
Historicism/Premillennial/Symbolic Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come and we will literally reign with him 1000 years before the new heaven and the new earth. After which we will literally live with Christ in heaven.
Historicism/Postmillennial/Symbolic Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come and before that there will be a great revival. After which we will literally live with Christ in heaven.
Historicism/Amillennial/Symbolic Earth – Revelations outlines the grand history of the church with some things still left to come (basically we are in the sixth bowl of wrath right now). Soon Christ will come but there is no need to expect a great revival before then. After which we will literally live with Christ in heaven.
Futurism/Premillenial/Pre-tribulation/Literal Earth – Chapter 4 onwards represents things that have not happened yet. The church will be literally raptured before all these literal horrors will take place. After which we will literally live with Christ on a new planet earth.
Futurism/Premillenial/Post-tribulation/Literal Earth – Chapter 4 onwards represents things that have not happened yet. The church will be literally raptured after some of these literal horrors will take place but before the worst parts. After which we will literally live with Christ on a new planet earth.
Futurism/Premillenial/(no rapture)/Literal Earth – Chapter 4 onwards represents things that have not happened yet. However the church will not be literally raptured before all these literal horrors will take place. They must suffer with the world until the second coming. After which we will literally live with Christ on a new planet earth.


Note 1: Mention of a great revival (above) in the future is usually thought of in connection with a conversion of many Jews and a subsequent falling away of many in the church just prior to the final judgment.

Note 2: Often these above positions can be blended a bit between them creating new variants.

I could spend months retrieving and cataloguing authors who have these views (some way more popular today than others) but this is not really practical simply from the fact that I have a day time job. Naturally I have over simplified each view due to the space I have allotted for the explanation and I have not complicated some of the futurist twists further buy the various roles that some feel Israel plays into the equation. Then again I am not even familiar with those details.