The irony of a cheater
Although Tarr is taken, he still openly competes for women's attention in the various salons and bars of Paris. That makes other gentlemen kind of unhappy, and Tarr ends up in multiple kinds of dishonor, having cheating on his fiancee with anyone he wants, basically. This is ironic, because Tarr is motivated by loneliness, but his behavior is perfectly isolating.
The ironic pain of indecision
There is a kind of suffering that Tarr allows throughout this book, even though it comes at a great cost to him: indecision. He suffers from indecision in his romantic life, but also in his inner thought life, in his career, and in his opinions of other people. Instead of just committing himself to an answer, his fear or responsibility makes him cower in commitment issues.
The ironic duel
There is a battle between two suitors at a bar, which is somewhat natural, one might argue, except that they are fighting about "honor" while neither have been honorable, and they are fighting over women, which is especially ironic, given that none of the men are exactly marriage material; Tarr doesn't even really want a marriage it seems.
The irony of two last characters
To introduce Rose and Prism at the end of the novel is certainly ironic and brilliant. When we meet Rose, the reader is asking, "Okay, well if he didn't settle for Bertha, but he also didn't go back to marry Anastaysa, then who will he marry?" Then we meet Rose, and it seems that is the answer—until we learn that he is cheating on Rose with some other random girl named Prism. This is ironic and maybe even mean, but in a playful way.
The irony of fun
Although fun is one way to enjoy life, one cannot privilege fun for very long, because so much of life is about sacrifice, responsibility, and grinding daily to meet one's goals. But in this book, we see people trapped by the illusion of fun. If there is a group of people going to a bar or dance, everyone goes, because it is fun, but by the end of the night, Soltyk for instance, knows differently. The novel seems to suggest that there is only so much fun to be had until it is time for commitment and responsibility.