Theologians usually define omnipotence as the "capacity to actualize any logically possible state of affairs." As you were saying, I agree with this definition because it avoids such quasi-paradoxes: clearly, even an omnipotent being (so defined) can't create a rock it can't lift any more than it could create an Euclidean triangle with a number of sides other than three. It just isn't possible.
I think the notion that an omnipotent being can do anything, even the illogical, is in itself illogical. It can't be asserted to be true because asserting so self-contradicts. Even Alvin Plantinga, brilliant theologian at Notre Dame, defends this position because otherwise you can have absurd positions such as an omniscient deity knowing that it doesn't exist and other nonsense like that.