To answer your question, we have to pose a few others: Is this a supernatural story or one of psychological horror, or both? Is Roderick Usher the only mentally ill character in the story? And how mentally sound is the story’s unnamed narrator himself?
To start with, it would have been easier to diagnose Roderick’s disorder if Edgar Allan Poe’s tale dealt purely with psychological horror. We could have assumed that Usher is either paranoid or schizophrenic, since he hears voices and imagines his house is a living, malignant entity. However, the very fact that the narrator also experiences uncanny, paranormal phenomena, such as a horrifying aura about the house of Usher that fills him with an “utter depression of the soul,” indicates that things are not just happening inside Roderick’s head. However, Roderick is in a state of extreme, nervous agitation, which has transformed his very appearance.
The now ghastly pallor of the skin, and the now miraculous lustre of the eve, above all things startled and even awed me. The silken hair, too, had been suffered to grow all unheeded, and as, in its wild gossamer texture, it floated rather than fell about the face, I could not, even with effort, connect its Arabesque expression with any idea of simple humanity.
Thus, his appearance and his agitated, frenzied behavior suggest that Roderick is mentally ill and in the middle of a major episode of stress. A hint that his illness is psychological in origin is revealed through a curious fact:
I had learned, too, the very remarkable fact, that the stem of the Usher race, all time-honoured as it was, had put forth, at no period, any enduring branch; in other words, that the entire family lay in the direct line of descent, and had always, with very trifling and very temporary variation, so lain.
This alludes to the fact that the Ushers have interbred through incest for generations to preserve the purity of their gene pool. Interbreeding to this extent would obviously predispose them to genetic mental illnesses.
Further, once we learn Roderick's beloved sister, Madeline , is dying, the basis for a diagnosis of acute stress disorder strengthens. Acute stress disorder often develops in response to an extremely stressful event, such as the death of a loved one. Roderick’s avoidance of Madeline, whom the narrator glimpses once when she is alive but is subsequently tucked away from view, suggests a classic symptom of acute stress disorder, in which the patient avoids anything about the source of the trauma. Because Roderick is traumatized about his sister dying, he wants to stay away from her. But a couple of facts keep us from a straightforward diagnosis of acute stress disorder: Madeline is not yet dead, and Roderick’s state of hyperactivity is not typical of sufferers. Neither does he shun social contact, as is typical in this disorder; instead, he actively seeks out the company of the narrator, inviting him to his mansion. Roderick's hyperactivity coupled with his...
occasional catatonia indicate that he may also have bipolar disorder. Moreover, I think he may share his mental illnesses with his sister, given the family history of interbreeding. Yet I think there is something more to Usher's mental state, and that "something" brings together the story's psychological and supernatural elements. I'm referring to Madeline herself.
In the story, the nature of Madeline’s disorder is unknown. However, based on the fact that she has lost all interest in life and is "wasting away," we can assume she has major depressive disorder. But how can she be dying from depression? Or is she even dying? The narrator is told of her dying by Roderick, but he himself does not have enough contact with her to make an independent assessment. This further complicates matters.
Besides, is the narrator himself reliable? Early on, we are told of his familiarity with opium, a substance known to produce hallucinations. His feeling of unease has been present even before sighting the house of Usher. Can we take his description of people and events at face value? The story’s end, with the peaking of its Gothic and supernatural elements, offers some resolution.
By now, Madeline has been dead for a week. She's been buried in a crypt in the house’s walls by the narrator and Roderick, a “smile” on her corpse. Roderick’s mental agitation has skyrocketed, and the narrator reads to him to distract him from a cataclysmic storm outside. But in a macabre twist, the storm’s effects begin to mimic the storm in the story the narrator is reading aloud. Roderick confesses at this point that he has knowingly buried Madeline alive. This cannot be just his imagination, because soon enough, the crypt splits and the narrator has an awful vision:
It was the work of the rushing gust—but then without those doors there DID stand the lofty and enshrouded figure of the lady Madeline of Usher. There was blood upon her white robes, and the evidence of some bitter struggle upon every portion of her emaciated frame. For a moment she remained trembling and reeling to and fro upon the threshold, then, with a low moaning cry, fell heavily inward upon the person of her brother, and in her violent and now final death-agonies, bore him to the floor a corpse, and a victim to the terrors he had anticipated.
Usher having been killed by his dying sister, the narrator flees the scene, leaving us with several unanswered questions: Is Madeline a vampire? Was Roderick trying to protect himself from her horror? Or do Roderick and Madeline take turns playing vampire and victim, manic and depressive? Or are they doppelgangers? Assuming the narrator is reliable, I would infer that Roderick does suffer from two real, psychological conditions—an underlying bipolar disorder and an acute stress disorder—but the traumatic trigger for his stress disorder in particular is paranormal. It is not Madeline’s death, as we assumed, but her resurrection. This melding of psychological and supernatural aspects is typical of Poe's Gothic realism.