Tom and Wilson's Friendship (Dramatic Irony)
At one point, Tom tells Mr. Wilson that he will sell him his blue car to help him move out west with his wife, Myrtle. The irony here is that Wilson wants to move because his wife is having an affair, but it is Tom who she is having an affair with. This is an instance of dramatic irony, because Mr. Wilson has no idea about the affair, and thinks that Tom is a kind, genuine man.
Daisy Killed Myrtle (Dramatic Irony)
The tragic end of the film is predicated on a case of dramatic irony. While the viewer (and Nick) knows that it was Daisy who was driving when Myrtle was killed, Tom and Wilson both believe that it was Gatsby who ran her over. Thus, when Wilson goes to confront Tom about Myrtle's death, Tom sends him in Gatsby's direction. Wilson shoots Gatsby in cold blood in his pool, thinking that he is enacting vengeance for the death of his wife. Gatsby faces the consequences for a crime he did not commit, and the disconnect between our knowledge of this and Wilson and Tom's belief in Daisy's innocence creates dramatic irony.
Tom the Brute (Situational Irony)
At the party at Myrtle's secret apartment in New York, she tells the story about how she and Tom met and how magical it was for her, that they were instantly compatible. Soon afterwards, Tom steps on her dog and Myrtle gets angry at him for keeping their affair a secret. The couple fights until Tom slaps her, giving her a bloody nose. This is an ironic turn of events, given how much Myrtle idealizes their special connection. The way that Myrtle characterizes their relationship and the way it plays out in person makes for a stark and ironic contrast.
Daisy Kills Myrtle (Situational Irony)
The fact that Daisy is the one who was driving when Myrtle is killed is not only an instance of dramatic irony, but also of situational irony, in that Daisy unwittingly kills her husband's mistress. While Daisy does not know the exact identity of the woman with whom Tom is having an extramarital affair, she knows that an affair is happening and that it is part of what makes her marriage so miserable. Thus it is an outrageous coincidence that she unintentionally kills the very woman with whom her husband is philandering. Ironically enough, Daisy hurts Tom without meaning to, by killing one of the women he loves.