stripping a poly strat isn't easy, there's a few guitar refinishing places on the web like;
they quoted me £250 to gold top a guitar and buffing the rest of the body, but that's a little different.. Since the undercoat/sealer on a strat is usually poly and the outter is poly I'd probably recommend keying the surface and painting right over the top...it'll make little difference and give you a pro finish since it's already a smooth prepped surface.
Nitromors is always fun (smother it, leave it in a black bag overnight and then see how long you can hold your breath while you scrape the gunk off), but sometimes just sanding it flat and painting over is the best route.
Unless you know it is a nice bit of wood underneath and want a trans finish etc. I think you'll pay more to have the poly removed professionally than it would cost to buy a new body...