The lawyer, Arthur Pym, is a reference to the only full length 1838 novel by E. A. Poe: The Narrative of Arthur Gordon Pym of Nantucket, in which Pym travels the oceans and lives through shipwreck, mutiny, and cannibals.
The joke about "a head on a platinum plate" is a reference to the 1841 Poe short story "Never Bet the Devil Your Head."
Each of the Usher children has a distinguishing color which can be seen in their clothes and home decor, and is most prominently featured in each of their death scenes. Prospero is red, Camille is white, Napoleon is yellow, Victorine is orange, Tamerlane in green, and Frederick is blue. These hues are a reference to "The Masque of the Red Death," though Flanagan appears to be following the color scheme of Roger Corman's film adaptation rather than Poe's short story.
Lenore calls Roderick "Grampus." This is a reference to the ship "Grampus" in Poe's only full length novel, "The Narrative of Arthur Gordon Pym of Nantucket".
While Lenore is scrolling through the Netflix menu to find a movie to watch with her mother, the movie Gerald's Game (2017) pops up. "Gerald's Game" is also directed by Mike Flanagan and features several of the cast from "The Fall of the House of Usher".