What are the ‘place prepared’ and the ‘greater works’ in John 14?

The Sunday lectionary gospel reading for Easter 5 in Year A is John 14.1–14. When I read this text, I cannot help but feel it has a slightly strange, dream-like quality to it, and I think that is for several reasons.

The whole discourse (which begins at John 13.31 and continues to the end of chapter 16) is dotted with apophthegms which are highly memorable—and often remembered out of context.
There are often abrupt changes of subject and sharp contrasts, even from one sentence to another (Judas leaving, but Jesus being glorified in John 13.31; Peter betraying Jesus, but the encouragement not to be troubled in John 14.1, and so on).
There is no obvious linear structure or progress in the discourse; instead, subjects are repeated, circled around, and returned to.
Jesus’ comments are often obscure or ambiguous, and the disciples are baffled—something that happens throughout the gospel between Jesus and his dialogue partners.
The disciples are experiencing Jesus’ comments from their own position, prior to Jesus’ death, and still without a clear understanding of what is happening and how it will be resolved. We are reading from a completely different, post-resurrection position, in which we know how the story ends. It gives us quite a different sense of engagement—a little like the difference between watching a film the first time, and being caught up in the emotion and drama of the characters as the story unfolds, and watching the second time through where the emotion has been dissipated because you know how it will end. This is particularly the case for us as we read in the Easter season, having been particularly focussed on the resurrection.
A further challenge in reading is that, for all these reasons, some of Jesus’ sayings have been commonly interpreted in a way that the whole passage does not really allow; we need to take the different elements together as we read the whole text.