In addition to what Rob said, the distinction is very subtle. I think the definition can be helpful...
IRONY -- the expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect
I think many people misuse the word "ironic." "Ironic" means something has to be contrary or opposite to what is expected or thought to be true. It's not a synonym for "weird." It's often used as a literary device.
Like Rob said...
SARCASM -- the use of irony to mock or convey contempt