The ironic dispossession
Lutie is dispossessed of a fortune in this book. When she was married to her husband, she had his income to rely on, which is good because in 1940, work options are very slim for black single mothers, especially in and around New York City. When he abandons the family, she is forced to do life as best as she can, with extremely limited resources.
The irony of Jones
Jones is an authority who wields his power in the most horrific way; he imposes himself physically on women who are not interested. He is also ironic because Lutie is doomed to him, unable to afford rent except on this street, the lowest of the low price wise, so she is left without much recourse. He tries to rape her at one point and fails, a sign of her absolute destitution.
The irony of power
It seems from this novel that life is most abysmal for those who are powerless. The power figures in this book, the madame of the whore house and Lutie's landlord, are both sinister, deviant folks who want to abuse Lutie for her beauty and her innocence. She is surrounded by the devilish agents of hell. Why? Because she is poor, and because she is perfectly disenfranchised from helping herself.
The irony of Min
Because Min isn't really Jones's wife, he doesn't actually feel vested in her, and he doesn't understand that attraction ebbs and flows over years in a relationship, so although he was extremely excited about Min at one point, he is now difficult to please, and frequently, he becomes extremely abusive toward her; she is the religious martyr of his journey into hatred and entitlement.
The irony of Junto
Who is Junto? His name means 'together,' but Lutie can never seem to get together with him. He's an interested suitor, according to Hedges, but he never seems interested in anything openly, only covertly through Hedges. Perhaps he is a rapist who pays her for victims. Perhaps he is a would-be savior; ironically, Lutie has to escape for her life before she finds out.