If things that are evil are against God's will, and they happen, how is this not thwarting his will and making God less than omnipotent? Keep in mind that Calvinists say God has two wills, a provisional will and a perfect will.
God is all-powerful because he holds all things in existence. Nothing exists without his continued will that it be so. But God is love by nature, and free-will is a necessary aspect of love. He cannot force people to do his will because it would go against his nature.
I was a Calvinist my whole life before I converted, and I don't remember anything about God having two wills. Can you point me to one of the Calvinist confessions or catechisms that explain this?
I still have problems throwing around "good" and "evil" as if they must mean something in an omniscient perspective. Is a hurricane or earthquake in itself an evil, or is it merely evil relative to the choices and preferences of human beings? Does this make sense? Why must we be constrained to an anthropomorphic vision of good and evil? Thinking moralisticly about the world like this keeps us away from a detached perspective which can lead to insight (think of what a scientist does, for instance).
An earthquake itself is morally neutral.
We need not go to the extreme of saying that every "act of God" is a deliberate action on God's part—ie, God is angry at Japan so he sends a tsunami at them (though I think this can happen, but I don't think it is the normative explanation for natural disasters). Neither do we need to go to the other extreme—ie, God set the universe into motion and sits back to watch like the god of deism. A lot of things in Orthodoxy require more nuance than these broad strokes.
A more nuanced, and I think correct, approach would be to say that sin has caused a breakdown in the natural realm. Natural disasters happen because of mankind's rebellion against God, and in some fundamental way that affects nature itself (because we are both noetic and material creatures, and each aspect affects the other). Our sin causes more stress upon nature, more pent-up energy, and as the world drifts further away from God's intent for it, it breaks down into chaos. While at Creation God created order from chaos, sin is changing it back into chaos.
It's like a bridge. When it is in its perfect and new condition, it is very strong and sturdy. But if pieces start to fall off, it gets rusty and cracked, soon it will collapse. This is because it went from the state of order (the creator's intent) to a state of chaos. That is what we see in mankind as well.
That is why, for instance, the holiest of saints can command wild animals and do other supernatural things. In their direct sphere of influence, the Fall is reversed and we get a tiny picture of Paradise once again.