I've got an Ibanez RG370DX (with an Edge III tremolo), and I was adjusting the action a lot today. I think, however, I may have been too abusive with the tremolo posts (which are adjusted to adjust the action) and now the whole where the allen wrench would enter has become almost rounded, making it almost impossible to turn.
What can I do to fix this?

I have heard of being able to replace it, but I can't help you there... Daniel Bowe pretty much summed it up, even if that could be considered flaming?
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and then there's free jazz, which isn't even for musicians.

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As my old guitar teacher once said: Metal really comes from classical music. The only difference is pinch harmonics, double bass, and lyrics about killing goats.
Go to a hardware store, find a dude that works there, ask them for an easy out set and tell him what youve done to your guitar. he should be able to explain how to use the easy outs and salvage your tremolo. then find replacement bolts.
Quote by Deltast0rm
So can the trem posts be replaced on an Edge III bridge?

sure if you can remove them anything can be bought and replaced.

specifically you now have the change to upgrade your trem posts to stronger ones.