Finch saving Violet
One of the most significant moments of situational irony is when Finch, the truly suicidal character, saves the life of Violet, the character at a momentary low. It turns our expectations on their head, but in a way that's important for the novel's message: if Violet were to save Finch, it would seem to indicate that she could save him from his depression, too, but Niven wants to be clear that she can't—no one can love away someone's pain.
Finch's discussion (or lack thereof) of his illness
Throughout the novel, Finch refers to his depressive episodes as "the Asleep" or his "black moods", and his stable or manic episodes as "the Awake." This is an example of irony in the dramatic sense—the audience, or in this case, the readers—understand that what he's talking about is depression and bipolar disorder. But this is unknown to the characters in the text. (Finch likely does know, but he never calls it by the names, therefore refusing to accept it. And when he tells Violet, he uses the same terminology, so she doesn't really know what he's talking about.)
Finch's father identifying his body
There is a cruel irony in the fact that Finch's father—his abusive, horrible parent who enacted lasting damage—is the one to identify his body after his death. The fact that Finch's body is so distorted that Violet says she can't even tell if it's him, but his dad didn't hesitate to say it's him, only drives home the point that he doesn't really know his son. Of all the people to do this action, his father is perhaps the least expected.
Bartlett students mourning Finch's death
Similarly, the fact that all of Finch's peers are mourning his death so openly after his suicide has a terrible irony to it. Not only did they not know him, they had been systematically ostracizing him all throughout his time in school.
