How does Hinduism deal with the fact that awful things, like Hurricane Katrina, take place without God stepping in to prevent them?
There's no neat, cut and dry answer to this, because Hinduism is a plural tradition. The basic difference between mainline Hinduism and other forms of theism--Judaism, Christianity, or Islam--is that Hinduism has the idea of karma. Karma is the sum total of an individual's actions, and the individual is believed to be responsible for it. God is omnipotent but has given human beings the freedom to do what they like and to reap the dessert of what they do. So ultimately, you might say, this limits God's omnipotence. If God in His omnipotence wants to wipe me out, He's limited by the fact that He has given me the freedom to be a moral creature, and if I am a moral creature than He can't wipe me out, by His own laws.
I am the master of my individual destiny, according to Hinduism. I have done things in the past as a result of which I am what I am now. How I act now and how I react to these situations will determine what will happen to me in the future. God is called the supervisor of karma. You might think of him as a judge who sees how people act and dispenses rewards or punishments depending on how they act.
This will happen to me irrespective of whether I believe in God or not--just as the law of gravity will influence us whether we believe in it or not. Given this situation, when a disaster like Hurricane Katrina happens the Hindu attitude is to look for what might the people have done to bring this on. This is a very delicate issue because it involves the question of moral causation and physical causation. Katrina is a storm caused by natural reasons. One school in Hinduism believes these natural events are a way in which karma works itself out.
What is Hinduism's attitude toward the question of whether God is omnipotent? Could He have stepped in to prevent tragedy?
There are two basic models of how God interacts with the world. I call them the architectural model and the creative model.
In the first, God is not the creator but the architect of the world, which would compromise the idea of God's omnipotence in the Western sense. That is, the atoms that make up the universe exist eternally along with God. So when God creates, He doesn't bring the universe into being out of nothing, but he brings the atoms together in such a way that the universe manifests itself. In this model, you can regard matter, human souls, and God all existing eternally. But the first two are dependent on God, and at the time of creation, God manipulates atoms to create the universe so that the souls can follow their course of karma in it. But the souls and the atoms have not been created by God. They have been their from the very beginning along with God.
Opposed to this is the creative model, in which God creates everything out of nothing, which is the classical Christian idea. The creative model gives more power to God than the architectural model.
Coming directly to the question of God's omnipotence, there are some schools of thought in Hinduism that believe that God may not be omnipotent, especially in some of his incarnations. Krishna, for instance, is involved in the negotiations to prevent the outbreak of the Mahabharata wars. He fails. Does it mean that God's power is limited? In this case, we have the answer of Krishna himself. He says sometimes God cannot avert a disaster. All He can do is damage control. And here again you see the working of karma. People have brought on themselves a certain condition. God cannot just overthrow his own laws.