Red (Situational Irony)
It is established at the beginning of the novel that "everything about [Geryon] was red," which may lead the reader to “see red”; to anticipate that Geryon is colored by rage. The irony here is that Geryon is actually a gentle and introspective soul who doesn’t erupt in anger even when perhaps he should.
Herakles and Geryon (Situational Irony)
In the original work Geryoneis, upon which Autobiography of Red is based, Herakles kills Geryon by shooting an arrow into his head. In Carson's version, however, the opposite is true—Herakles loves and supports Geryon—until it isn’t, and Herakles breaks Geryon’s heart. The situational irony here is about the unexpected; first that Herakles isn’t the villain that we anticipate, and then that he becomes the villain in an unanticipated way.
Justice (Verbal Irony)
The novel’s main section “Autobiography of Red: A Romance” begins with the line "Geryon learned about justice from his brother quite early" (20). The verbal irony here is that Geryon is abused and violated by his brother. His brother teaches him about justice through enacting an injustice that mars Geryon’s psyche for life.
Joy to the World (Situational Irony)
During their relationship, Geryon and Herakles often sing the song "Joy to the World," which they refer to as "their song." The situational irony in the contexts in which they sing is how often Geryon is unhappy while they’re singing it.