1 Henry is already dead
The movie begins after Henry died. Everything Henry experiences in the movie is an after death experience where he was moved to a different world where people have to repent for their sins.
2 Selena killed Henry
Henry died after his wife Selena realized he was cheating on her with Rebecca. If you focus at the very beginning of the movie while Henry is waiting for the car, you will see him remembering the sound of the gunshot that killed him after Selena told him that she loves him.
3 Henry's wound was the gunshot
The strange wound Henry had since the beginning of the film was the wound that resulted from the gunshot that killed him earlier. At the end of the movie, you will notice that this is the area he holds after getting shot.
4 Henry must be purified
The world Henry is in is an intermediate world that people who sinned have to go through so that they can get purified before they are sent to heaven. Henry needs to be purified of the sin of lust before he can move to heaven.
5 The cycle keeps repeating itself
The cycle Henry goes through keeps repeating itself until he repents for his sin properly by accepting to be burned with fire. Henry's sin was lust, so according to Mr. Remiel, he has to repent by being burned. (See The Illusionist (2006) Movie Explained)
6 Henry saw versions of himself
Some of the bodies and strange creatures Henry saw in the house were nothing more than versions of himself that failed to repent during previous attempts. The man who hanged himself was actually Henry in a previous attempt.
7 Henry saw other people suffering
The other people Henry saw were other sinners who were paying for their sins in different ways. The nurse, for example, was full of pride in her earlier life and so she had to serve others to repent. (See Oblivion (2013) Movie Explained)