I wanted to start this thread, because I fear I'm derailing another one, and also, I want to clear up terms.
I've learned a while ago, that when someone uses terms like "omnipotent" or "all powerful", that I need to figure out exactly what they mean before discussing things any further with them. If I don't, we end up talking past each other for several posts before one of us figures out the problem. That being said, when people use these terms, they tend to take one of two meanings:
1) All powerful. There are no limitations on God. He can even circumvent logic without it being a logical contradiction.
2) Really powerful. More powerful than anything in the universe, but with certain limitations.
Approaches of theodicy:
When discussing the problem of evil (why does evil and/or suffering exist in a world with an all-powerful, all-loving god?), there are many different ways to reconcile this. The whole topic is called Theodicy. That being said, all responses could be summed up in one of three ways:
1) Somehow limit God. These types of defenses assume God has some sort of limitation. So, Free Will assumes that it is more important that we have choice rather than to not suffer; God can't give us both. "You have to know dark to know light" assumes that humans can't appreciate heaven without knowing something lesser, first, and this is a limitation that God works inside. "The best of all possible worlds" assumes that this is the best possible configuration of things, and if something like Tay Sachs didn't exist, the world would be a worse place.
2) Give a non-answer. This is basically asserting an answer that assumes it is true on its own. Answers like "mysterious ways" and "master plan that we can't possibly comprehend" fall under this category. They could both be summed up as "I don't know, but I'm sure there's a good reason". These answers aren't necessarily wrong, but they aren't really testable, either.
3) Redefine omnibenevolence. This approach is basically to change the concept of what people normally assume when they think of "all good" or omnibenevolent. Some people may find these new definitions disturbing, and others may find them comforting. So, when asked a question about "why did children die in the flood?" or "why did God kill children during the 10th plague?", responses might include "God created people/souls, so he has dominion over them and can kill them if he wants to." or "The dead children will end up in heaven, so it doesn't matter if they die on Earth.". How anyone receives this approach will vary from person to person.
And that's really it. There aren't any other approaches.
Implications of "all powerful" on theodicy:
Now, to get back to omnipotence, if you use the definition of "really powerful", then the first approach to theodicy listed above still works just fine. It relies on God having some limitations, but God can still be "really powerful". However, if you use the "all powerful" definition (as in, God has no limitations on his actions), you lose the ability to use the first approach. You likely lose the ability to use the second approach, although you can still use the third approach. Let me explain this a bit better:
So, if God has no limitations on his actions, nothing outside of God can force him to act in a certain way. If we don't accept this, then we are using the "really powerful" definition, and not the "all powerful" one. So, under this paradigm he can even circumvent logic. If someone asks the old "create a rock too heavy to lift" problem, you simply say "yes, he can create it, lift it, and not create a contradiction because he's God." God could have his cake and eat it too without it being a contradiction, or even resorting to cloning his cake. He's just that powerful. That being said:
Free Will would no longer work, because a God with no limits could give us free will and have us always make the right decision, and it wouldn't be a contradiction (see rock too heavy to lift of cake and eat it too, above).
"You have to know dark to know light" is a defense predicated on a limitation. The idea is we have to know suffering to appreciate Heaven, and there's nothing God can do about this. This is the best way he can get us to be externally happy in Heaven. So, this defense no longer works.
"The best of all possible worlds" also is based on an explicit limitation. The idea is that God has everything configured this way because it's the best possible way, and will yield the best possible results. If he were "all powerful" as defined above, he would not be limited in such a way.
Mysterious ways/master plan we can't comprehend is a bit more muddy, in that the actual ways or plans are never revealed, but rather are assumed. Still, any plan or action taken would be one that God wanted, because there is no limitation to his actions. So, even if we don't define what those actions are or what that plan is, it cannot involve God being limited by an outside force or framework.
So, I think that clears up what I've been trying to say in the other thread. If you feel that my three categories of theodicy are inaccurate, please, tell me why. Other than that, I think I've summed up why the available approaches of theodicy are directly linked to how one defines "all powerful" or "omnipotent".