Treating Greg to Ice Cream (Dramatic Irony)
When Greg is torn up about whether or not he should take the blame for terrorizing the kindergarteners on Safety Patrol after Rowley has been misidentified as the culprit, Greg's mom sits him down and advises him to do the right thing. But since she doesn't know the situation, Greg tells her he did do the right thing. She takes him out for ice cream to celebrate, creating dramatic irony because we as readers know that in fact Greg took the immature route and decided to let Rowley get in trouble for something Rowley didn't do.
Campaigning for Treasurer (Situational Irony)
Greg runs for class treasurer since he wants to have the ability to give money to things girls want and screw over the jocks, but when it comes time to campaign, he doesn't run on his own merits. Instead, he chooses to run a smear campaign against his sole opponent, and has all of his signs taken down for telling lies. Ironically, Greg is running for a position that would require honesty about finances, but he's effectively disqualified from the race for trying to win on dishonest terms.
"What a lovely soprano!" (Verbal Irony)
Mrs. Norton says this to Greg when he's trying out for the school play. Ironically, Greg tried to sing poorly so that he wouldn't make it through the auditions. Doubly ironically, everyone who tries out for the play gets cast, so not only does Greg have no way of getting out of the play, but he also has to suffer the fact that Mrs. Norton thinks he has a lovely singing voice.
The Red Sweater (Situational Irony)
Equal parts dramatic irony and twist of fate, Greg's mom accidentally gives Greg the sweater that she meant to give to someone through the Giving Tree, and gives that person at the Giving Tree the video game that she meant to give to Greg. Since Greg puts a lot of stock into both Christmas and video games, it's ironic that his mother gives away his video game and that he's such a poor sport about it that he's resentful that someone in need got a nicer gift than he did. The twist of fate element comes in because Greg is so self-centered that the only way someone would get a nice gift on his behalf is by total accident.
