There are three kinds of verbal irony: sarcasm, overstatement, and understatement. The Odyssey is short on sarcasm and understatement; as a work from the epic tradition with elements of science fiction fantasy, it is heavy on overstatement:
In book XII, examples are as follow:
Speaking of the Scylla and Charybdis, Circe says this to Odysseus:"Here not even a bird may pass, no, not even the timid doves that bring ambrosia to Father Jove, but the sheer rock always carries off one of them, and Father Jove has to send another to make up their number; no ship that ever yet came to these rocks has got away again, but the waves and whirlwinds of fire are freighted with wreckage and with the bodies of dead men." No ship has ever gotten away? Hmm... Sounds like overstatement to me...
Circe says this Odysseus, who wants to fight Scylla and Charybdis: ""'You dare-devil,' replied the goddess, you are always wanting to fight somebody or something; you will not let yourself be beaten even by the immortals." Always fighting? I think not... More overstatement.
She also says, "Neptune himself could not save you." Hyperbole, exaggeration, verbal irony.
The sirens likewise use verbal irony: "No one ever sailed past us without staying to hear the enchanting sweetness of our song- and he who listens will go on his way not only charmed, but wiser, for we know all the ills that the gods laid upon the Argives and Trojans before Troy, and can tell you everything that is going to happen over the whole world.' " No one? Overstatement.
Then Odysseus says, "My Friends, this is not the first time that we have been in danger, and we are in nothing like so bad a case as when the Cyclops shut us up in his cave." Not the first time, huh? That's an understatement!