Amoral describes something without morality, or without a sense of what is right and wrong.
Immoral describes an act which KNOWINGLY goes against morality, or KNOWINGLY chooses wrong instead of right.
So a snow storm can kill a child, and a man can kill a child. But the snow storm is an amoral event and the murder is an immoral event (usually, right? See last paragraph).
It is easy to describe things as "amoral" when you talk about nature. Things like floods, or storms, or forest fires can be very destructive, but we would never describe them as bad moral choices because nature doesn't "decide" to do these things. However, it is much more complicated when you want to describe human events. In fact, I don't believe you can describe human events as being strictly "amoral" in the sense that absolutely NO moral choices were made. Morals are present in all our choices, aren't they? We don't really use the word "amoral" in the strict literal sense when we talk about people and their choices. When we say a person is "amoral" we usually mean they don't share our PERSONAL moral code. In other words, they are without OUR morals. For example, people will say that "bankers are amoral predators" or "soldiers are amoral killers". Neither of these accusations are strictly correct because both bankers and soldiers can follow strict moral codes.
The word "immoral" is much less complicated. It implies that there is a moral code which a person decided to break or ignore. But then again, we can make the question complicated by asking.."is it immoral to kill a man? What if he is about to kill another man?"
But now we are talking about philosophy. In English literature there are many thought experiments which we can use to discuss these ideas. Like, for example, the Trolley Problem..