“God can do everything.” For philosophers Omnipotence is a much more difficult concept. If God can do everything can God lie? As usual the Bible is contradictory. here. Can God sin? Can God limit his own power? Can God do what is logically impossible.
Basically it seems that Christians extend or limit God’s imaginary power as suits them. Different Christians have different concepts of omnipotence.
- this phrase, "God can do all things," is rightly understood to mean that God can do all things that are possible
Under this view, God chooses not to lie or so on due to other reasons, not limitations on his power (e.g. he may not lie because he it is in his Nature, or so on). Alternatively the God of the Bible may lie as the Bible is contradictory about that  and many other matters. 
Traditional Muslim theology, on the other hand, has largely rejected philosophical contemplation (Falsafa and Kalam), and to the extent it handles these issues tends to see God's omnipotence as transcending mere human logic. As to how this makes any sense, a good answer might be Bila Kayfah ("without regard to how").
Judaism traditionally tries to avoid commiting to any theological conceptions, but Orthodox Judaism generally asserts that while God can do lots of things, He has chosen Hiddeness, largely so as to allow humans to make free-choices, i.e. to preserve their free-will. The precise limits of God's powers in-principle are far less agreed upon, but in a sense the Jewish answer to the ancient question "Can god make a stone that He cannot lift?" is answered by "Well, He created a stone He would not lift - Free Will, which He won't break; whether He can is a more speculative point".
Perhaps the solution to the problem lies not in God's ability, but rather in his character. Can he make a rock so big that he cannot lift it? Perhaps. But that would be the extent of the rock's ability and God could easily fix this. So the real question is, Would he?
More generally, and in all the three Abrahamic religions as well as in others, omnipotence is perceived in many ways by many sects and schools of thought, often differenly by the same person at different times.