The TONE of a literary work entails the attitude with which the story is being narrated. It is an attitude that shows the underlying feeling toward the subject, a character, or a situation.
In "The Open Window," there is a consistent, underlying tone of mockery that stems from the characterization of Framton Nuttel. His narrative is rife with mentions of a nervous condition that is unique in that it is aggravating, even to his own sister.
..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..
There is no compassion toward Framton despite of his condition, which makes the reader wonder if Roald Dahl is being cruel, or humorous. Given that his style is one to never pass on a chance to be sarcastic, ironic, or dark in humor, we should read the commentary on Framton, and his situation, as a comical one where a young woman takes full advantage of a much older- and much weaker- man.
From that point, the other tones come from the nested tale of the supposed trip that left three men and a dog nowhere to be found. For this story, Vera adopts a dark, thrilling, and frightening tone that aims to scare Framton, thus making his condition even worse.
Framton's own tone is nervous, inconsistent and frazzled. At no time does he change his tendency to make himself vulnerable, and this leaves the reader almost chuckling in the end, when Framton finally loses it and takes off running out of the house.