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I've always found it hard work to differentiate ironic/sarcastic/paradoxical/satirical... The differences between some of these words in certain cases is pretty fine.



Easier by example:

Irony: The mascot of Wu's Chinese laundry/shirt irony is one of those rumply dogs.
Sarcasm: "I've seen prettier faces on iodine bottles."
Paradox: Arnie built a time machine that fell on his past self when he went back in time, killing him, so he could not have later built the machine...
Satire: Etaoin is still waiting for the other shoe to drop.