Dorian,
The more I consider that curious "TO HUMANS" bit you included, the more I wonder what is your argument with me.
My position is that the omnipotence paradox is a useless argument against theism because the theist has two outs by which it does not apply. They may simply declare their god above logic, a declaration which renders further logical discussion with them impotent. Or, they may declare that the definition of omnipotence used in the paradox is not the definition they believe applies to their god, so its refutation of omnipotence is irrelevant.
Indeed, the last out is one many theists do take, stating that omnipotence does not entail the ability to do the logically impossible (and sometimes other caveats, as well).
Now, your assertion that an omnipotent being can do things that seem logically impossible to humans implies that such things are not actually logically impossible, but that humans lack the capacity to understand the logic involved. As such, there is no problem with paradox, because our omnipotent being is not contravening logic, merely surpassing human understanding of it. All this does is provide the theist yet another out. The point still stands: the omnipotence paradox is a useless argument against theism.
My argument with you is basically that you have a particular definition of omnipotence, and anyone who uses a different definition you dismiss with phrases like 'not worth arguing with' and 'no serious theist'. In other words, you resort to
ad hominem attacks rather than attacking the position.
You keep saying that if someone holds that their deity is beyond logic, etc., that there is no point having a logical discussion. But that presupposes that you can always have a logical discussion about beliefs! Beliefs of this sort are literally irrational, i.e., they are based on faith, not necessarily reason.
Ultimately, our difference lies with the definition of omnipotence, and I insist that for someone to be truly omnipotent, there must be no barriers whatsoever, no limits whatsoever, to that omnipotence, including logical contradictions, etc.
To go way back to the OP (remember that?) I interpreted the thread title as having a silent 'if he existed'. Thus, I would say that if God exists, he would be omnipotent, and therefore there would be nothing he couldn't do.
Note, our argument wasn't whether God existed, or even if an omnipotent being existed, but what an omnipotent being would be capable of. As I said before, an omnipotent being would be utterly and absolutely limitless without exception, by definition.
Had our discussion turned to whether an omnipotent being existed, I would have insisted that one could not. However, in light of what I have been saying, I'd have to say "I don't know". That's still not to say that this being would be aware of or give a crap about us, or even exist in the same dimension or state of awareness as we do.
Bottom line: An omnipotent being is possible. My belief in a magic sky daddy is not.