I had no idea what 'OPP' stood for as a kid, which is funny, because it's right in the lyrics, but I was too young to understand what that meant. So I, too, would just belt that song out whenever it came on. Nobody stopped me, either.
I'm pretty sure there's never been an official definition for what it meant. I believe they claimed it stood for "other people's problems" back in the day while other people said "other people's pussy."