Here's the way I learned it from a priest. God is omnipotent, which most people take to mean "all-powerful," that is, He can "do anything." But, what omnipotent may mean is "most powerful." God can do anything that is actually possible to do. Thus, it would by logic be impossible for Him to resolve a contradiction, such as making a rock so heavy He could not lift it, and that sort of nonsense. Nor could He somehow cause 2 + 2 to add up to 5, since it would entail an absurdity.
Can God kill himself? Obviously not, since it would be impossible for a non-existing being to bring himself out of existence.