Irony is usually in the form of a situation - that is, an ironic situation. It is when two things contradict each other... Yes, when situations are contradictory. Or, when a situation is "funny" because it is not what one would ordinarily expect.
For example, a traffic warden being issued a parking ticket... This is "ironic" because a traffic warden issues people parking tickets for a living, and hence you would not expect him to receive one, so for him to receive one is ironic.
Sarcasm is in speech, and it is a form of speech that is clearly insincere. It is very common in Britian, and it is usually used for emphasis.
For example, you point out something very obvious like "it is hot in the summer."
I respond, "oh, really?!" in exaggerated astonishment, and my astonishment here is sarcasm; I know it is hot in the summer, so why are you telling me this?
Another example:
I am terribly ill and incessantly coughing; you, quite stupidly, ask me, "oh! Are you sick?"
I sarcastically respond, "no, I am just great!"
Of course I am not great - I say I am sarcastically.
And what is the reason for my sarcasm? It is because you asked a pointless question to which you already know the answer.
Also, there is satire, and this is essentially comedy and humour. Mockery can be another way to describe it.
I am sorry if my examples are poor, but I hope the above helps you understand!