Nazi Youth with a Progressive Mother (Situational Irony)
Part of the dark humor of the premise of the film is the contrast between Jojo and his mother's politics. This contrast is itself ironic, in that Jojo, the 10-year-old kid, is a serious wannabe Nazi, and his fun-loving mother has more progressive politics. This is a reverse of the dynamic we have come to expect between parent and child. Ordinarily, we would imagine that the parent is the one with the more serious and conservative political philosophy, while the child is trying to rebel against that. In Jojo Rabbit, it is Rosie the mother who must keep her politics hidden from her humorless and despotic son.
Elsa (Dramatic Irony)
After Jojo discovers Elsa, the Jewish girl, living in his attic, he must keep her existence a secret from the other people in his life, fearing that if the Gestapo discovers that his mother is hiding a Jewish girl, they will kill her. Thus, a dramatic irony occurs, in which we the viewer know about Elsa's hideaway, but the Nazis with whom Jojo interacts in his daily life do not.
Additionally, there is a dramatic irony in the fact that Jojo and Elsa do not tell Rosie that they know each other. Rosie believes that Jojo does not know that Elsa is living in the house, when in fact they are becoming well acquainted. In this instance, we know something Rosie does not.
Elsa Scares Jojo (Situational Irony)
Another bit of situational irony is the fact that Elsa, the Jewish girl living in Jojo's house, is scary to Jojo. While she ought to be the one who is afraid of him because he is a Nazi, she is quite tough and intimidating and scares the little boy quite a lot, which is rather ironic.
Jojo and Yorki's Sweetness (Situational Irony)
One of the ironies of the film has to do with the way that Waititi has cast the Hitler Youth. Jojo and Yorki are played by two particularly adorable and sweet-looking children, and their friendship is a sweet one. The contrast between this marked sweetness and the fact that they are training to become Nazis is a comedic irony that is used as a gag throughout the film.