The Free Will Defence
Technically this is a defence and not a theodicy, as this doesn't give a reason for God allowing suffering, but give God a possible reason. I think that difference really isn't much different to other theodicys as they are all trying to solve a mystery. The argument holds that God has created this world that has the potential to do both good and evil. To remove evil He would also have to remove good. Humans are able to love, but they are also able to kill, hence the existence of moral evil. The same could then be applied to natural evil as water is needed for all living things, but it also means it is possible to drown. Hot and cold air cycles are need for our weather patterns, but it also allows the possibility for tornadoes.
Alvin Plantinga is a big supporter of the free will defence with moral evil, I am not sure what he thinks on natural evil (my Encyclopedia of Christian Apologetics talked about natural evil in this way).
In both cases of evil it seems that God is distance in His creation. Like the Deist God in the 19th Century, God has wound the world up like a pocket watch and has let it go. It seems that God loses some of His sovereignty as He doesn't decide to act on His creation. Surely God could act in a way to reduce the amount of suffering in the world, without negating the freedom people have. Also what about those who do use their freedom for evil, surely God should intervene and restrict their freedom.
God should also loses credit for "saving" people in disasters. If God is responsible for saving people from disasters He is also responsible for killing all the other people who didn't survive. With this free will defence, it is the rescue crew who saved the victims, as God allowed them the freedom to choose do their job. If you credit God with allowing people the choice of doing good, you must also credit God with allowing people the choice of doing evil. Ultimately I think this God is still responsible as He allows people the freedom to act. His passive will is still involved.
So there still is a tension between God's sovereign control and our free will. I am still unsure if Alvin Plantinga holds to Compatibilism or Incompatibilism, as he is a bit hard to read, eg in this article he says:
I am inclined to think the notion of moral evil implies the notion of libertarian freedom; that is, it is necessary, I think, that anyone who commits moral evil, has or has had libertarian freedom with respect to at least one action. (p621)But he concludes with:
So even here I resist being committed ... to libertarian creaturely freedom. (p624)While Walls writes here:
It is not altogether clear whether or not Plantinga himself thinks he is required to accept libertarian freedom. (p375)and then on the next page:
the issue is not whether Plantinga actually believes in libertarian freedom. It is clear from his writings as a whole that he does.