Some examples of irony in "The Gift of the Magi", "The Necklace", "The Cask of Amontillado", and "The Ransom of Redchief" are presented below:
In "The Gift of the Magi" we find dramatic irony. This means that the reader knows what is going to happen, but the people in the story do not.
We know that Della is selling her hair to buy her husband, Jim, a chain for his watch, but she does not know that Jim had sold his watch to buy combs for her hair which she had sold. That means that the gifts, although expensive, were useless, but they showed the love Della and Jim had for each other.
The irony in The "Necklace" is situational irony. The main character, Mathilde, and her husband worked ten years to pay for a fake necklace that they had lost, not knowing that the necklace was worth a little bit only.
In the "Cask of Amontillado" the reader knows that the villain of the story, Montresor, is going to murder Fortunato, but the victim does not know this himself. Fortunato's name derives from the word "fortunate" which means lucky, but he is not lucky at all. Cask can mean either a barrel that holds wine or a coffin. At the beginning of the story, the reader may think that the story is about tasting wine in a cellar, but we quickly find out that it is a murder story.
The irony in "The Ransom of Redchief" is that the Bill and Sam, two kidnappers, planned to make money from kidnapping a kid, but in fact they lost money trying to get rid of him. From captors, Bill and Sam, become the captives of the kid.
Irony is the literary device that is used in all the stories that I mentioned, and it is what makes these stories more interesting.