Assumption (Verbal Irony)
Alcée asks Calixta if she "remembers in Assumption." This refers to an old sexual encounter of theirs, where they similarly gave in to their basest desires to plumb the depths of ecstasy. The irony here is that Alcée is making a double entrendre, an 'assumption' that Calixta—who has a husband and a child—will want to repeat the same acts of passion that the two embarked on all those years back in the town of Assumption.
"Enough sense to come in out of a cyclone." (Verbal Irony)
When Calixta worries out loud about the safety of her husband and child out in the storm, Alcée responds, "Let us hope, Calixta, that Bobinôt's got sense enough to come in out of a cyclone." It's an ironic line, because it undercuts Calixta's maternal worry with logic, but also because Alcée also had the sense to come in out of a cyclone, and it led to the current seduction.
Clarisse's Free Breath (Dramatic Irony)
When Clarisse receives a letter from her husband Alcée at the end of the story telling her to feel free to stay in Biloxi with the children for another month if she wants to, she welcomes the opportunity as, "her first free breath since her marriage," that "seemed to restore the pleasant liberty of her maiden days." The irony here is that Clarisse is enjoying the freedom of being away from her husband as much as Alcée has enjoyed the freedom of being away from her.