Irony, on a basic level, means 'disguise' or 'pretending', i.e. saying one thing and meaning the other.
Sarcasm comes from 'ripping the flesh apart' and means something that is meant to be hurtful and biting.
Sarcasm and irony can be combined together of course, but they're not the same (and sarcasm isn't a stronger version of irony).
Irony can be sarcastic, but not every sarcasm classifies as irony.
Suppose someone is trying a dress that makes him/her look fat:
"How do I look in this dress?"
- Irony: I think it accents your figure pretty well. (i.e. and doing so it makes you look fat, which is what I actually mean.)
- Sarcasm: You look disgustingly fat.
- Irony + sarcasm: I don't think you look disgustingly fat in this dress.