Given a set of distinct points in 2D space, and a rectangle (coordinates of all four points, sides parallel with xy axis) how can I quickly find which points are inside the rect
Along with other answers, you can also look into Morton codes (z-order curve sorting).
In your case, that is static data, you can even represent the whole point data as an array.
https://en.wikipedia.org/wiki/Z-order_curve
This paper also have a rather complicated timeline of different "multi-dimentional access methods" --http://www.cc.gatech.edu/computing/Database/readinggroup/articles/p170-gaede.pdf