The Irony of Captain Hart
The town of St. Francisville celebrates an annual festival on the Day the War Stopped, which happened to honor a war veteran who died, giving him a proper ceremonial burial. Olivia notes the irony: the captain killed himself and was honored, while her mother killed herself and was shamed, and her daughter is still feeling the effects of the latter.
The Irony of Jamie's Escape
Olivia and her friends help Jamie escape from the scene of the crime in order to protect him from jail and even possibly the death penalty. However, in New Orleans, Jamie is killed, which is the same or even a worse fate than the one he would have suffered if he had stayed and faced the consequences of his actions.
The Irony of Parents
Three of the main characters (Olivia, Jamie, and Maggie) have serious parental troubles; their parents are terrible for different reasons. Olivia's mother committed suicide and her dad all but abandoned her, Jamie's father is an abusive alcoholic with fits of rage, and Maggie's mom abandoned her to pursue a failing career as a folk artist/drug addict. Despite this hatred, each of these characters can ironically recognize their parents' flaws in themselves - Olivia has a pull toward the water, Jamie has rage problems as well, and Maggie has inherited her mother's artistic talent and fierce, independent nature.
The Irony of Mr. Benton's Abuse
In his bouts of drunken rage, Mr. Benton physically abuses his wife but has never actually laid a finger on Jamie. This treatment ironically makes Jamie the instigator in the fight that ends in Mr. Benton's death: he was the first one to ever physically assault the other.
The Irony of Dr. Green's Treatment
Olivia draws criticism for spending too much time in the graveyard, reflecting an unhealthy desire to stay in the past and refuse to move on. Ironically, the treatment prescribed by Dr. Green (her therapist at the novel's end) recommends that she go back to the graveyard in order to speak to her mother at her gravesite.