To answer the slightly vague question "How does imagination play a crucial role in the story of "The Fall of the House of Usher?" two points have to be cleared up. The fist pertains to the definition of "imagination." If by "imagination" you mean characters or author creating mental images of sensory things that are not present (Random House Dictionary, Dictionary.com), then, for the characters, the answer is none because all things turn out to have been founded in actual experience. But for the author, we must suppose his imagination wholly created mental images of sensory things that were not present. On the other hand, if by "imagination" you mean the Romantic construct wherein "imagination" is a higher order of reason that governs rational thought and gives order and metaphoric meaning to the world, then, in relation to both the characters and the author, imagination does play a crucial role in "The Fall of the House of Usher."
The second point to clear up pertains to the interiority or exteriority of the phrase "in the story." If by "in the story," you mean within the fictional setting of the story, then imagination plays no role because every perception of both the narrator and Usher was proved at the end to have basis in reality. If by "in the story" you mean through the author's creative process, then imagination does play a crucial role because Poe constructs a plausible world in which unusual philosophical ideas are dramatically explored.
To further the discussion, let's suppose that by "in the story" you mean within the setting of the fictional story and by "imagination" you mean the Romantic era construct built by Shelly and Coleridge from Aristotelian principles. Thus consideration of "imagination" is restricted to the governing function of reason that creates metaphoric meaning and orders sensory perceptions. Further, "in the story" is restricted to the characters Poe created and eliminates discussion of Poe himself.
Imagination as defined above plays a crucial role pertaining to the characters in Poe's short story "The Fall of the House of Usher" in that 1) the story is an exploration of how the mind orders perceptions, 2) the central thesis of rational discussion between the characters is the idea of the sentience of vegetation, 3) Madeline's end is a dramatic examination of the connection between the cessation of imagination and life. To illustrate the first point, some of the narrator's first remarks are about his perceptions being in opposition to his expectations: "I had so worked upon my imagination [reason] as to really believe..." a perception that he otherwise held to be impossible. The most detailed description of the conversations between the narrator and Usher covered the the idea of Usher's perception of sentience in the vegatable domain.
To illustrate the second point, this conversation was detailed because it presents the central thesis between the characters, whether vegetation can have intent and can drive a family to ruin, as Usher's song chronicled as being the demise of the House of Usher. Regarding the third point, Madeline's strange end examines the connection between catatonic unconsciousness and death. In the case of the Usher's, the connection was proven to be unsound: Her reason (imagination) had deserted her leaving her in a state of catatonic unconsciousness, but death had not yet visited her, hence, her grisly appearance at the chamber door.