Trawling around recent Olympiad threads I seem to find quite a few which you've posted. Kudos to you for paying attention to what is a far more worthwhile academic challenge than normal high-school exams.
My first comment would be you seem to be focused in maths (why else take it early, including STEP), so why the disinterest in the Maths Olympiad? It is usually recognised that the IMO is the highest of all Olympiads - the hardest to qualify for and by far the deepest in terms of the problem-solving skills needed (and a match for any of the others in terms of theory). But you're focusing on Bio and Chem Olympiads instead?
(I say this as someone whose main focus in my high-school years were the Chem and Physics Olympiads. I could never have done well in an IMO. But then ... I'm not planning to study maths!)
Analysis is an interesting subject you may also find worthwhile to start with. (I mean simple functional analysis of course - for example the question
For each of the following sequences of functions on [0, 1], indexed by n = 1, 2, . . ., determine whether or not the sequence has a pointwise limit, and if so, determine whether or not the convergence to the pointwise limit is uniform.
1. f
n(x) = 1/(1 + n
2x
2)2. g
n(x) = nx(1 − x)
n3. h
n(x) = √nx(1 − x)
ncopied straight from a current math problem sheet, which you may even be able to answer now!)
University study often commences by looking at vectors and matrices but I personally would not recommend that.
If your goal is the Olympiads you may not need to worry about the deep subtleties in the derivations of physical chemistry laws (though they do exist and may occasionally crop up in Olympiad questions). However, I would recommend a thorough study of (if you're in the UK you'll already know this) Chemical Structure and Reactivity (Keeler and Wothers), Physical Chemistry Vol. 1 (Atkins), a chemical thermodynamics book (e.g. Advanced Engineering Thermodynamics by Smith & Van Ness) and a kinetics book (e.g. Reaction Kinetics by Pilling and Seakins), a detailed organic chemistry book (Klein explains well but Clayden is needed for good detail), at least 1 inorganic chemistry book (you could try Vogel Qualitative Analysis, it's pretty thorough). Analytical chemistry will still remain; standard books do not really cover it in IChO depth; you can try learning it from practice problems, but might be best off just leaving it until you qualify. Same for biochemistry (you won't need much of that anyway so I could recommend a book, but why bother? - it doesn't come up hugely).
I'd probably recommend the books in that order, because IChO is seriously physical-heavy. Get on that Keeler & Wothers, Atkins and perhaps Clayden ASAP - even after that you'll need loads of practice. For any details missed, the Oxford Chemistry Primers usually mop up pretty good (on the same topics as above) and should be an easy read in terms of concepts once you've read the corresponding main texts!
I might see you if you do make the team, and good luck.