"MY aunt will be down presently, Mr. Nuttel," said a very self-possessed young lady of fifteen; "in the meantime you must try and put up with me."
Here, with this quotation, starts the suspense. With Saki's simple opening come two important questions to the reader's mind. The first is how self-possessed can a young lady of fifteen actually be? The second is why does she say "must try and put up with me"? Our interest is piqued and our attention is fine-tuned to see what peculiarities to come will answer the questions and explain her words.
The very next sentence introduces irony.
Framton Nuttel endeavoured to say the correct something which should duly flatter the niece of the moment without unduly discounting the aunt that was to come.
In addition to situational irony, the narrator's ironic tone is manifest. Ironic humor is evident in the narrator's choice of using repetition to describe Nuttel's conversational predicament: "duly flatter the niece ... unduly discounting the aunt."
Both suspense and irony center around what is soon introduced to the reader's attention. First, the narrator tells that Nuttel notices that an "undefinable something about the room seemed to suggest masculine habitation." Next, the self-possessed niece mentions her aunt's "great tragedy" that "happened just three years ago."
For the duration of the short story, the young lady weaves a tale of her own that builds upon the masculinity of the room and the "great tragedy" and centers around the open window of the title:
"You may wonder why we keep that window wide open on an October afternoon," said the niece, indicating a large French window that opened on to a lawn.
Just a note about the sort of window taking center stage in the story. French windows come in two types and both extend from near the ceiling to the casement at the floor. In either kind, entering or exiting requires a small step up and over the casement that holds the window when closed. One type, the type I imagine in this story, is a single wide pane of glass (perhaps secured in lattice working) that is raised up or lowered down; it can be seen in manor houses in some British movies filmed on location. The second type, with which most are more familiar, has two less wide panes of glass that open and close by swinging apart and together at the middle; these are commonly called "French doors" in America.
The suspense of the story for Nuttel--and for the reader--is whether two men long lost to human knowledge will walk through that open window. For the niece, the suspense is anticipating Nuttel's reaction and the depth of it. For the aunt, there isn't much suspense as she isn't in on the story woven by her self-possessed niece; her experience is more one of bemusement and wonder at Nutell's behavior.
The irony of the story is that the men will walk through the window precisely as predicted as the niece has devised her story to precisely coincide with their routine habit. A second irony is that the niece, who is self-possessed, uses her self-possession to such great disadvantage for other people! The ultimate irony, of course though--and this irony adds the overarching sad tone of the otherwise amusing short story--is that while Nuttel has come on holiday for the health and restoration of his nerves, the young lady is completely shattering his nerves with a devious tale contrived solely for her own amusement.