You can't huff and puff and blow logic away.Unless reality is clay in your hands and you can change what is or isn't logical on a whim. A limited and finite god would be as constrained by the rules of logic the same as all of the rest of us, but an infinite god bends logic over the table, fucks it up the ass and then has it whip up a square circle while it's making him a sandwich. Logic is an omnipotent god's bitch.
It doesn't respond to force. It can't be bent.
The problem is trying to apply this concept of "infinity" to something beyond mathematics. By what logic do we say it can be done?
If you're omnipotent, you can huff and puff and blow logic away as easily as you can do anything else. You're the irresistable force and everything else is a less-than-immovable object. If you decide on a whim that two plus two also equals five, then when you add two and two together, you get both four and five at the same time in a completely consistent and logical way simply because that's how you've decided that reality functions.
Logic is essentially just a methodology for discovering proofs of how it is that the universe works. If someone, in his infinite power, changes the way that the universe works then the logical proofs which are built off of how the universe currently works will change along with it. If God decides that two plus two equals five and you sit there trying to get to four by putting two groups of two things together, you're going to fail everytime and you'd need to split one of those groups in half and add one and three together if you wanted to get to four, since it doesn't work with two and two anymore. You could fume about how you think that's illogical all you like, but observation beats theory every time and you'd be championing an invalid logical proof which doesn't match up to what empirical reality has now become.