God and Logic
What we call "laws" of logic are actually descriptions or explanations of how reality operates. Aristotle, it is said, didn't "invent" logic; he "discovered" logic.
Having said this, let's turn to this question: Can these "laws" be violated or "broken"? Well, since these "laws" are not some "force" which rules over us, but rather descriptions, I would say that there is nothing to violate. Logic is not some entity or being with power that could be "denied."
Let me state this another way: If something (anything) exists in reality (or if any statement corresponds with reality), then it must exist in a certain way. This "certain way" is described by humans through logic.
For example, take the law of non-contradiction. A contradiction CANNOT be true - not because some "law" is lurking overhead imposing its will on us, but because if something exists in reality, it must behave a "certain way" (i.e., "logically"). I cannot be alive and not alive at the same time and in the same relationship - such a notion is a contradiction, and is thus absurd. I am either alive or not alive. I can't be both at the same time. Notice that the statement, "I am both alive and not alive at the same time and in the same relationship" isn't really saying anything at all! What idea is it communicating? It's communicating NOTHING, which is what a contradiction is in reality (like I said, the statement is absurd).
After saying all this, let's discuss God (I'll discuss an "omnipotent" God like the Jews, Christians, and Muslims all claim). The Bible says that "all things are possible with God." As far as I'm concerned (some theists would disagree with me), the phrase "all things" does NOT apply to such "things" as contradictions, because a contradiction is NOTHING (no thing). A contradictory statement is absurd, because a contradiction cannot be true; that which is contradictory simply IS NOT. The phrase "all things" applies to all THINGS (which, to me, implies everything that IS and nothing that IS NOT).
Can God make a "square circle" or a "four-sided triangle"? No, because a "square circle" is not a thing (a "square circle" simply is not). Reality, whether we speak of God or man, is what it is, and logic describes how reality is. Contradictions are not possible, even for God.
Does this negate God's "omnipotence"? Not at all. The Bible doesn't say that God can do that which is contradictory. When the Bible discusses the "omnipotence" of God, it refers to God as the one being who has no equal, who has power that is unmatched, and who is so much greater than anything else that exists. It doesn't get much better than that.