The key to this answer about Madeline and Roderick Usher in "The Fall of the House of Usher" is in the narrator's description of the family tree:
I had learned, too, the very remarkable fact, that the stem of the Usher race, all time honored 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 vaiation, so lain.
Furthermore, the narrator states that he considers this deficiency is in "perfect keeping of the character of the premises"; that is, the lineage and deficiencies run parallel to those of the mansion of the Ushers itself. Thus the "appellation" of the House of Usher connotes both the family and the mansion.
Part of the Gothic effect of Poe's story comes from the aberrant union of all the elements: character, setting, atmosphere. The fraternal twins are so alike in their deficiences that they seem to be merely alter egos of the other. Sharing so much of their genetic makeup, they react to one another; there is a type of extrasensory communication, as it were. [Modern studies have revealed that twins often communication with one another in indefinable ways.] For, while not knowing exactly what transpires with Madeline after she is placed in her coffin, Roderick, nevertheless is so disturbed and unnerved, that his psychological illness becomes exacerbated.
Thus, their rather bizarre relationship seems to be physical in the sense that, having such a limited genetic makeup and being twins, they are the male and female forms of essentially the same person; it is of the spirit, too, as they share sensations and have an extrasensory communication. When Madeline dies, so, too, does Roderick "fall," along with the mansion which has so long housed this limited genetic line since all are the House of Usher.
A lot of people do speculate that the relationship between the twins is incestuous. However, we do not see anything in the story that would demand that this would be true. They do seem very close (their health seems to be connected to each other, for example), but that could just be from being twins.
I'd say the effect of their relationship is to help kill Roderick. You can argue that he dies because of the sickness that afflicts his sister. His condition gets worse as hers does and they end up dying together.