The Satire of The Book of Jonah
Some of the comedic elements are:
1) Jonah is told by God to go to Nineveh and immediately boards a ship going to Tarshish. Tarshish was literally the edge of the world. Jonah's disobedience is completely on display, but given a humorous twist. The idea that one could run from God is in and of itself ridiculous. The idea that one runs as fast as they can the other direction from where God is sending them, is hyperbolic. Jonah is presented as supremely silly and sinful. God's love and protection for Jonah is absolute, however, despite Jonah's disobedience. God's grace is extreme in this book.
2) Jonah is sleeping during the storm. The shipmen are all amazed at how Jonah could possibly sleep through the storm that his battering the ship. Jonah is not scared. Why? Because Jonah knows that God is going to take care of Him. Jonah is completely unconcerned for the safety of the others on the ship, but he is confident that he has nothing to worry about. Jonah knows, and later his belief on this matter is justified, Jonah knows that God is going to take care of him. The indifference of Jonah is amplified by the contrast with the ship's crew, who do all they can to avoid sacrificing Jonah even when it has become clear that this is the will of Yahweh. That the men try to outrun God on Jonah's behalf, while Jonah cared for them not at all makes, in a humorous way, the clear point that Jonah is not a very good guy, and that people who are not Jews can be good people.
3) Jonah is thrown in the sea and saved by a fish. Jonah's trust in God was absolute, and the book makes clear the crazy lengths God goes through to save His people. Jonah doesn't need to ask for forgiveness, He is simply saved, and in a rather crazy way. Christians often paint the fish as some kind of punishment. But in fact, Jonah's prayer makes it clear that the fish was a grace, a saving miracle. Jonah is in the belly of fish, and thanks God for His being swallowed. That in and of itself is pretty funny.
4) The actions of the Ninevites as they try to repent. They put sackloth on their animals and even include their animals in the fast. It is a humorous way of showing the depths of faith non-Jews are capable of. It also shows that the Ninevites are not simply evil, they are silly and a bit dim. They don't know God well enough to know what to do. So they do silly things like make their animals uncomfortable.
5) Jonah is mad about the death of the plant, but is angry at God for not killing the Ninevites. He understands love, but won't extend it to those he thinks are undeserving. Jonah is again on display as being a pretty bad dude. God doesn't remove His grace, even at this point. God's message to Jonah in the end is in essence, "The Ninevites are stupid, Jonah. They are so stupid. But I love them, just like I love you." The connection between God's love for the Ninevites and His love for Jonah is clear. For as the Ninevites are silly and stupid and sinful, so is Jonah. Thank you God for loving the silly, the sinful, and the stupid. I, for one, would be in trouble if you didn't.