Verbal Irony: The china
When Bugs and Bud eat food at the Hooverville, "A woman handed me and Bugs each a flat, square, empty tin can. 'That, m'lords, is your china. Please be careful not to chip it'" (69). This is an amusing bit of verbal irony on the woman's part because she is handing the boys a cheap tin plate and teasing them that it is "china" and they should not "chip it." She's making light of the rundown conditions of the shantytown.
Situational Irony: White people at Hooverville
One would assume that people, regardless of their race, would know they needed help if they were poor, out of work, deprived of their home, and bereft of their savings. However, the white family at the Hooverville maintains that they do not need help because they are white. This is ironic, of course, because they need just as much help as the others present, and their white skin does not preclude them from sharing in the country's collective misery.
Situational Irony: Herman's Identity
It is an excellent example of situational irony that Herman turns out to be Bud's grandfather, not his father. Because of Bud's beliefs and Herman's responses, it makes sense, for most of the narrative, to assume that Herman is Bud's father. Thus we are surprised when he turns out, instead, to be his mother's father.
Situational Irony: The Room
It is also ironic that Bud ends up sleeping in the room that belonged to his mother, because he is initially scared of the room because of some sense he has of the previous occupant; but it turns out that the previous occupant was his mother—precisely the person whose memory is most comforting to him.