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In short: Homography relates two views of a set of coplanar points. The essential (E) and the fundamental (F) matrix relate two views of a set of points that don't need to be coplanar. The difference between E and F is that E only works for pairs of points whose image coordinates have been normalized beforehand - their raw image coordinates have been transformed by the camera matrices you get when you perform camera calibration.
For a stereo pair, the intrinsic parameters are the ones related to the cameras themselves, that is their respective distortion coefficients and calibration matrices. The extrinsic parameters are the relative rotation and translation between the cameras.
If you could tell me a bit more about what you'd like to - what is your input data and what projection matrix you'd like to compute - I might be able to help a little more.
