The irony of family distance
Although family seems to imply closeness and intimacy, this novel features the opposite side of family. This family is somewhat rallied, but only by death in the family. When Laurel discovers what she has been missing, there are affairs and dysfunction in many of the family's marriages, and Fay's confession about her deceased husband are enough to make any sensible person cringe. This family is not a close-knit team, by any means.
The ironic epiphany
When Laurel leaves the swampy underworld of Louisiana, she has an emotional epiphany: That life is so beautiful, not in spite of the darkness in the world and in her family, nor in spite of the grim reality of death; rather, she feels life is beautiful because of life's horror and confusion. She sees the family as a third person visitor, but not a disinterested one. She feels deeply connected to this family, but in a way, she can see the situation from a bird's eye view.
The irony of Fay's affair
The irony of an affair is obvious: One could even argue that perhaps marriage exists to extinguish that kind of behavior from one's life. But, instead of growing through sacrificial love, Fay's romance was insulated by her husband's money. She notices in the aftermath of death that she has "gotten away with it," but in light of the death itself, she is unnerved by the likelihood of responsibility. She admits that for years, she desired for him to die.
The irony of religion
Mardi Gras is a symbol for the irony of religion, which is stated so eloquently in the ancient Tao Te Ching: "Take away religion, and people will do the right thing." The novel portrays the Catholic season of Lent as a burdensome obligation, so daunting that the town revels on "Fat Tuesday," which is what Mardi Gras means, in a kind of Bacchant revelry. It is the opposite of the religion's intent, one could argue. But yet, the imposition of strict religious strictures are what drive the behavior, so religion is ironic in the novel.
The irony of love
When Laurel tries to share her own feelings and experiences, Fay ignores her, becoming rude and impatient. Clearly, she wants to talk about her feelings, but it has not occurred to her that there might be a reason to care whatsoever about anyone other than herself. Why should she? By being selfish, she literally got everything she ever wanted, for free, essentially. Why should she care about Laurel? As Laurel reflects, it is clearly love that Fay desires, but she has ostracized herself from love by becoming vicious and selfish.