Verbal irony is defined simply as a statement of contradiction, such as when a person shouts, "I'm not upset", when obviously he is. It can also be when someone says something that is hypocritical or paradoxical.
For example, when Cyclops shouts out, "Nobody hurt me!", this is a contradictory statement. He means the individual who calls himself "Nobody" (Odysseus), but it sounds like no single person hurt him.
When Odysseus refers to the Cyclops as "lawless and inhuman", this is hypocritical. Odysseus has already told the story of what happened at the city of the Cicons:
There I sacked the town and put the people to the sword. We took their wives and also much booty, which we divided equitably amongst us, so that none might have reason to complain.
This is inhuman treatment, but Odysseus doesn't recognize it.
Also, Odysseus talks about being too clever for the Cyclops:
but I was too cunning to be caught in that way
In reality, it is Odysseus' foolishness that get him and his men "caught". When well away from shore, he shouts back to the Cyclops his real name, not only providing a target for attack but providing the Cyclops' father, Poseidon, with the name of whom should receive punishment for having injured his son.
When Odysseus tells Polyphemus his name is no body and he gets poke in the eye and comes out screaming " Nobody hurt me!"