The irony of love and war
This novel begins with the archetypal struggle to win the girl. Both Jim and Dave desperately love Daisy, and that brings out a natural urge to fight for her, like animals. They do fight, and the portrait is ironic, because for love, Daisy encourages hatred between the men. Also, the irony of love itself is present, that not all infatuation leads to love.
The petty churches
Ironically, religion is strictly depicted for its tribal, cult-forming aspect, because the two small town churches immediately pick sides and settle into a kind of trench warfare between churches. That runs contrary to the intention of the church to bring peace and unity, and picking sides and condemning the "other" is exactly what Jesus tells the Pharisees not to do. They are ironically petty and divided, for the same reason that Jim and Dave fight. They're human.
The irony of exile
The exile is ironic because it is almost like the community said to Jim: "You're not ready yet; you need to go on a two year pilgrimage as a wanderer." The ironic verdict might remind some readers of the Cain and Abel story where Cain kills Abel and is forced to become a wanderer. The motif returns in Coleridge's Rime of the Ancient Mariner. Ironically, Jim grows from this punishment, because he experiences life outside of his community. The banishment helps him.
Daisy's ironic authority
The men feuding for Daisy believe they are competing for a role of authority in Daisy's life, because of their opinions of gender role. That's why Daisy's authoritative decision is ironic when she says whoever will work for a white man, that's who she'll pick. This ironic authority is a narrative depiction of the power that women have because of selection. They will pick who they like more, and the men are ironically subject to her decision.
The ironic freedom
Daisy's authority gets completely shattered, though, because her decision is to compel her husband into a kind of slavery, working for minimal pay for a white man who will inevitably profit from that labor. When the men hear this, they suddenly don't want Daisy at all anymore. Why would she want to weaken and emasculate her husband? Their desire for freedom, autonomy and respect is revealed to be far more important and powerful than one girl's opinion.
