Situational irony plays on our expectations of what should be or what will happen by having something different or opposite occur. An example of this story's situation irony comes from the presupposition that being in a quiet country setting will help Mr. Nuttel's shattered nerves to heal. In fact, the opposite occurs, as Vera's ghost story leaves him more shattered than ever.
A second example of situational irony is Mr. Nuttel's sister's assertion that he will better off visiting people in the country than being on his own. She says,
you will bury yourself down there and not speak to a living soul, and your nerves will be worse than ever from moping. I shall just give you letters of introduction to all the people I know there.
Ironically, Mr. Nuttel would have been better off by himself.
The chief example of situational irony is Vera's elaborate fiction about her aunt's "great tragedy." Our expectation is that people tell the truth and, moreover, don't behave maliciously, especially with a person who is vulnerable. The seemingly kind Vera shows she is anything but sweet and helpful to Mr. Nuttel by telling him a false story that drives him away. The irony is that Mr. Nuttel takes her at face value. It doesn't occur to him that she might want to be rid of him or harm him.
Dramatic irony occurs when the reader knows something that a character or characters in a story do not. In this case, the reader has learned what Mrs. Sappleton has not: that Vera is a liar. Therefore, Mrs. Sappleton seemingly accepts Vera's fantastic explanation of Mr. Nuttel's sudden departure:
he told me he had a horror of dogs. He was once hunted into a cemetery somewhere on the banks of the Ganges by a pack of pariah dogs, and had to spend the night in a newly dug grave with the creatures snarling and grinning and foaming just above him.
Verbal irony occurs when an utterance means the opposite of its surface meaning. This occurs in the last sentence, when the narrator drily observes that
Romance at short notice was her [Vera's] specialty.
Horror and cold-blooded malice are actually her specialties, even if she might believe otherwise.