Yes, it does seem odd. I was completely thrown by anyone asking about demonology, which means exactly, "The study of demons". That's different than the second part of your question about how demons work in the world and what sort of natural phenomena could be attributed to them.
I think I need a nap already.
Before my eyes clank shut, we can get rid of the first part and the last part of your question. I think no one should study demonology. There is such a thing because the belief in, or fear of, demons has always been a part of human history. The idea that demons are ruining one's life is as prevalent in the life of a savage living on a remote island three feet wide as it is in the parlors of the tea sipping cultured and it always has been, even before the invention of tea sipping. As a result, there is "a lot" to know about what humans have thought about demons, from the ancient Assyrians, Greeks, Iranians, Persians, Chinese, Israelis and all the way up to Christian culture. The Assyrians and the Iranians, in particular, had elaborate demonologies.
But it's not something you really need to look into, unless you're some kind of theology/history major and you have a test coming up on Azazael and a paper due entitled "Who Is Liltith?"
The problem with the actual study of demons is that, for our intents, the information is full of theological errors. In other words, you will be up against heathen legend vs. Christian theology. It would be very difficult to sort it all out on your own. St. Albert the Great has some advice for you: "It is taught by the demons, it teaches about the demons, and it leads to the demons."
Demons do not control natural phenomenon, so you can let that go. One might argue that the devil might have some effect on what happens "because" of natural phenomenon, though. We'll come back to that.
That leaves us in the middle. What's the deal with the devil?
The devil is a fallen angel. Fallen from where? Heaven. God's favorite angel, Lucifer, decided one day that he should be equal with God. This is a problem. Angels are pure spirits, all good and holy and very, very smart. But only God is God. So Lucifer's uprising backfired and all the angels that went bad with him went to Hell with him.
"I have to stop here for a moment and reflect on the outlandish silliness that is "Satan worship". The whole reason" that Satan "is" Satan is that he is "not "equal to God. So why are you worshipping him? Crazy. Just the other day at the grocery store I saw a lady dressed as some sort of vampire. It's "August", so we know she wasn't trick or treating. This was a style choice.
Sad.
Anyhow...where was I? Generally speaking, when we say the "devil" we mean Satan (formerly known as Lucifer) and when we say "demon" we mean any of those other fallen angels. The Catholic Church teaches that Satan and his pals are alive and well and they are relentlessly trying to grab your soul. How do they work in the world? Against you, that's how.
"This makes it very, very hard for us, because we really, really don't need Satan's help to sin. We are weak enough on our own. But here comes Satan and his demons to make it even harder. It's bad news. These aren't just some kind of crazy little monsters with pitch forks running around giving people flat tires so their days start off badly. These are fallen angels". They are very smart beings. Satan doesn't have to waste his time trying to get you to watch more television and not eat your vegetables. Satan can take a look at the evil in the world, that evil we perpetrate all on our own, and "orchestrate" it. That is his power.
So did Satan cause Hurricane Katrina? No. You'll have to ask a meteorologist what causes a hurricane. But did Satan help in the aftermath of stranded souls and carpetbagging? I'm quite certain he did.
Credit: master-of-tarot.blogspot.com
