The irony of marital romance.
The ironic depiction of marriage in this novel is it's greatest ironic feature. Essentially, marriage exists for men to have women like property, meaning that the wives are often repressed. Some of the most important characters in the story would have been women, if not for the constant demands of marriage in a misogynistic community. The consequence of this irony is that there are lots of affairs, which goes against the conservative identity of the town.
The irony of racism, or the Bea Sorenson story.
The irony of racism is that a person like Bea ends up being mistreated. Bea is a Swedish man who lost his wife and child to a tragic death, and how does the town repay him for his suffering? They make him leave. Their racism was willing to tolerate a normal-looking life, but when Bea's circumstances become abnormal, they make him leave, instead of being there for him in a very difficult time.
The irony of misogyny, or the Fern Mullins story.
The irony of the Fern Mullins story is that her behavior is easily judged, but similar behavior is condoned when men do it. Think of the millionaire who tries to manipulate Carol into an affair. Does that result in expulsion? No, but Fern's indiscretion does end with her being forced to flee. The irony is that in the moment, it felt so easy for the town to unanimously reject Fern for completely normal human indiscretion. (The question of statutory rape notwithstanding–the story only indicates that actually, Cy and Fern were fairly close in age, so it's not clear what the social standard for a situation like that might have been in the 1910's.)
The irony of motherhood.
The irony of motherhood is that for a woman like Carol, motherhood does two opposite things: One is that it provides meaning and interest to a boring repressed life. But simultaneously, it worsens the woman's shot at equal treatment. She finds that motherhood should be naturally wonderful, but in the context of societal mistreatment, it's not as easy as it could be.
The irony of inequality and daily life.
Because life is difficult for everyone, sometimes it is difficult to notice systematic injustice, because sometimes life just sucks, regardless of the systems. But the novel does a brilliant job of showing cycles of behavior that consistently mistreat certain kinds of people, namely women and foreigners. The irony is that Carol thought her problems were rooted in her personality, but they were actually rooted in the judgmental attitude of the dominant majority.