Besides satire, what are other types of humour in literature?
Some examples from the Bible...
Because I am not sure what you would or would not count as literature, allow me to address a more specific question: "What types of humour are there in the Bible?"
Sarcasm: Isaiah 44:9-20 talking of the folly of worshipping gods made with hands says "Shall I bow down to a block of wood?"
Exaggeration: Matthew 23:24 Jesus speaking to the teachers of the law and Pharisees says: "You blind guides, straining out a gnat and swallowing a camel."
Situational comedy: In Matthew 14:13-21 we read the account of the feeding of the five thousand. Note that the disciples come to Jesus and ask him to send the people away to find food. Jesus says they don't need to go away "you feed them!". A moment of some discomfort for the disciples. Funnily enough, that's exactly what they end up doing.
Word play: Matthew 19:24 Jesus says "Again I tell you, it is easier for a camel to go through the eye of a needle than for a rich man to enter the Kingdom of God". The word play here is not visible in the English, but the word for "camel" is similar to the word for a thick rope such as used to anchor a boat.