One example of irony comes right at the end of the story. Framton Nuttel has run out of the house, terrified by what he thinks are ghost people and a ghost dog. The audience may expect that Vera would "come clean" and tell her aunt and other relatives that she had told Framton a story and scared him away. However, contrary to the audience's belief, she tells yet another story about how Framton has a fear of dogs after being trapped in a grave with snarling dogs around him all night.
This is situational irony because the irony is only caused by the situation the characters are in.
There is verbal irony in The Open Window by Saki, because Vera talks about a "tragedy" that had occurred; however, she knew that the "tragedy" was a lie, when Framton Nuttel believed this story to be true.
You can tell that Vera is lying because at the end of the short story, Vera mentions how Mr. Nuttel had developed a fear of dogs, so must of been afraid of the spaniel. The reader heard the only conversations between Vera and Mr. Nuttel, and it never mentioned anything about dogs...
What the names in The Open Window mean relative to the content of the story:
Mrs. Sappleton: "sap" = fool; believes anything or taken advantage if easily
Framton Nuttel: "framton" = frantic , "nut" = crazy
Vera: "ver" = veer people off in the wrong direction , "vera" = truth (so there is irony within the names as well).