I personally would use bleach as it has the power to disinfect (I don't think oxy clean has anything about killing germs on it's label), and staph is something I wouldn't want to mess around with. Just make sure you do some extra rinses afterwards.
Found this online, which also recommends bleach and hot drying:
My son had a little staph on his bottom where he'd had a boil that burst and got infected. I boiled all our inserts and then ran everything through the wash with oxiclean. Then I washed with Charlie's Soap 2-3x, followed by 3-4 plain hot washes to make sure all the solutions and (hopefully) infection got totally rinsed out.
We haven't had any further problems, so I assume I got it all.