Is it OK to use solid oak flooring on top of a plywood subfloor in my shed?
Man I hate saying this because I just love when people reuse things and even the bigger bonus for using it in a creative way but I personally wouldn't.  Sounds like you have a lot of leftovers.  I would try to use them elsewhere in the house or sell them for others to use.

My problem with putting it in a shed is that the oak planks don't handle water well, it isn't an easy install (for a shed), it will look dirty really quick (lots of cracks), and as the other answer points out you will need to put a few coats of poly (2 not enough in my opinion for outdoor use).

Now if this shed is merely a very nice room not in the house I could see it, maybe.  Given that you will keep dirt and moisture out.  If it is a true shed that will house tools, garden equipment, pottery, and things like that then I think the oak flooring is impractical.  Also it would be a shame if you laid this down and it started buckling on you due to changes in temperature, humidity, water/gas/oil spills...  I see high risk with little reward given that the shed is used for what most sheds are used for.