I've done all four endings. They all have mild variations in epilogue.
*Heavy Spoilers (Epilogues) will be strike through*
Dust and Silence occurs when you are "too" abusive to Asterion, choosing every dialogue to avoid or harm him.
The player tricks Argos, and Asterion refuses to follow the player's orders. Asterion and Argos (revived) leave the hotel universe together to live a better life, the hotel runs empty and Hermes will come to clean it up upon P and Storm's arrival and kicks them out, the player dies.
Shackled occurs when you are abusive towards Asterion, but not too much so, and agree to Argos' plan
The player pushes Asterion into the crater, effectively being minced by the wooden statue, the player falls for Argos' plan, and dies in front of Argos. Argos rescues all parts of Asterion and heals him. Argos encourages Asterion to be selfish, Asterion leaves the hotel by himself, and Argos takes his place, the pelt that he used to wear becoming sentient and molding to Argos' skin as he is now the prisoner. P and Storm stumble upon the new prisoner and interrogate him.
Welcome to the Minotaur's Hotel occurs when you are not as abusive to Asterion, and trick Argos.
The player pushes Argos into the crater, and is thought to be dead. The player drinks the poison in front of Asterion, and dies. Asterion returns to the fridge you found him in, P and Storm discover Asterion and interrogate him. Asterion becomes manic and lashes out at Storm and P and collapses. Storm and P offer to help him up and talk in the bar. It is not known whether P and Storm find what they're looking for or whether they become the new hotel owners.
As you are, I once was occurs when you make no promises about cooperating with Argos, and not "too" abusive to Asterion.
The player ignores Argos' plan, and tells him to never appear again. Asterion follows the player back to the hotel and lives out the rest of his days in the empty halls of him and Asterion, presumably torturing him. The player returns to the bus stop he obtained The Deed from, but rather finds himself in place of the old man and offers The Deed to a younger man with no defining features, presumably the next player as you become more senile.