If you want to install plywood, then 1/2" is the way to go. No need to use anything thicker. As Chuck says, you still need to address the high seams in the OSB by sanding flush. Then for MAXIMUM insurance, glue and screw the plywood down into every joist, as Chuck suggested. I wouldn't waste my time or money but you certainly are welcome to. BTW, I repaired and refinished a floor that I installed in 1990 over one of the first OSB subfloors I'd seen. That subfloor had been rained on, swelled up, dried out and I still installed the oak floors using staples. That floor was fine EXCEPT for the french doors leaking and the water damaged that ensued. The lesson here; OSB should not be a problem. Architects are specifying it all the time and the NWFA and NOFMA have decided it is an acceptable substrate.
http://www.nofma.org/installation1.htm
http://www.nwfa.org/member/pdf/Sect2.pdf