Here's an example of irony, and it ties in to how this thread was started. In The Post Thread VI the topic of politics was started. I mentioned that my latest assignment, had to do with politics. I have to choose one of the amendments and defend it. It is ironic that 2 days earlier, I was given the assignment. To simplify, irony is similar to a coincidence.
Now sarcasm. I can be very sarcastic at times and here is an example. I will be getting ready to go to my job, which I hate with a passion, and I will change into my work uniform. Suddenly my sister, whom I share a room with, will come in while I'm changing and say, "Are you going to work, Maureen?" and usually I will answer, "No, didn't you hear, wearing work uniforms are the newest trend now! Everybody's doing it! Of course I'm going to work, baka!"
That's sarcasm. Hope that helps.