Logic is not constrained to human conceptions but is objectively valid. One has to keep in mind that logic is based on premises and inferences. Given the premises and inference rules, the conclusion automatically follow.

So a four sided circle cannot exist because we have defined circle to be a particular shape. A valid four sided circle would need a change in the definition of circle itself. But then we're not talking about the same thing anymore. Similarly, the same universe cannot contain both an irresistible force and an immovable object, because of the conflicting definitions of those terms.

Even an omnipotent God is constrained by logic. In a reality without logic, it'd meaningless to try to understand any aspect of reality. God can both exist and not exist at the same time. He can be both Good and Evil. Conscious beings can be both alive and dead. It is hard to see how a illogical universe can retain any meaning that we attribute to God and Creation.