Mister Nuttel has arrived at Mrs. Sappleton's for the purpose of rest and relaxation to calm his nervous state. From the moment he arrives the niece sees to it that he remains on edge. Her description of the "tragedy" sets the reader up for the entrance of the aunt which, of course, makes Mr. Nuttel and the reader question her sanity.
When the three men and the dog come walking through the window the surprise is too much for Mr. Nuttel and he flees the scene.
The final irony comes as the niece comes up with yet another falsehood about Mr. Nuttel and his fear of dogs from having to spend a night in a "newly dug grave" hiding from a pack of dogs. We see how incredibly mischievous she really is.
The main irony in "The Open Window" is in the fact that Framton Nuttel is a hypochondriac who has come to the country seeking complete peace, quiet, and rest, but instead he ends up in a household which appears to be haunted by ghosts carrying guns and greeted by a hostess who appears to be insane.
A second irony is in the fact that the hostess Mrs. Sappleton sends her fifteen-year-old niece downstairs to entertain Framton. At this age Vera will be getting training in becoming a housewife who will need to know all the little arts of entertaining visitors and acting as a gracious hostess herself. (It is logical that Vera should have been sent down ahead of her aunt because Mrs. Sappleton would be dressing more formally to greet the visitor, who might have arrived unexpectedl; whereas Vera is only a child and wouldn't need to make any special preparations to talk to a visitor for just a few minutes.) Vera may have been getting too much instruction in company manners and is feeling rebellious. Instead of playing the junior hostess and making polite small talk, Vera invents a story that ends up scaring poor Framton half to death. His nerves may never be the same.
It is hard to think of a third instance of irony that would be comparable in importance to the two just discussed.