The situational irony is that they each gave up there most valued possession in order to get the other a gift her hair and his pocket watch the irony is that he sold his pocket watch to get her something for her hair and she sold her hair to get him a chain for his pocket watch
I the story the husband sells his watch to buy his wife some combs, and she sells her hair to buy him a chain for his watch. The irony in the gift exchange is critical to the story, because the theme is that they did'nt mind getting useless gifts, because they knew their partner gave up something important to them (his watch and her hair) to but a gift for each other.
