Omnipotence
I think the Catholic church has an interesting definition:
"Omnipotence is the power of God to effect whatever is not intrinsically impossible."
http://www.newadvent.org/cathen/11251c.htm
This gets around the old "square circle" objection. I would define it more like "nothing is too difficult for God." Ah Lord GOD! Behold, You have made the heavens and the earth by Your great power and by Your outstretched arm! Nothing is too difficult for You Jer. 32:17
However, there are many things God *will not* do, such as become evil, or illogical, or do anything inconsistent with his character. That is why I think this question about "How can an omnipotent, omnibenevolent God allow people to suffer in hell for eternity" is not all that well-formulated. But, I think "omnipotent" is still a good word, if properly understood within the character of God. So, nothing is "too difficult," but some actions He will never take, so they are in effect, never going to come from him. It is not a matter of weakness but of consistency of character.
I think it comes down to the balance of God's attributes: if God were to allow unrepentant sinners into heaven, or even have mercy on them after they have rejected forgiveness through his son, that would be inconsistent with his character, because he is just.
I'm also still thinking that this word "omnibenevolent" is not really an accurate way of describing God, depending on the definition, because it implies that God could never let anything bad happen. God is perfectly good and loving, but he is also just and holy, which is part of his goodness. If we use this word, then we cannot fail to define it, because it sounds like it could mean that God will never do anything that we dislike, because those are the things that seem "good" to us.
Better words would be "holy," "righteous," "just," "perfectly good," and "perfect." Sorry none of those have "omni" in them. :oP To be "omnibenevolent," if I understand the definition, God would never punish anyone or let anything bad happen. "Shall we accept good from God, and not trouble?" Job 2:10
Google "omnibenevolent," and you see that it's not used by Christians much.
Certainly open to discussion.