The Memory of The Order is its own creature, there are not multiple forms, and there is only one.
It appears to be wearing a leather jacket, along with goggles, brown boots, and a black and red respirator. It carries two circular-shaped, rusty blades. Even though it carries these weapons, it does not attack Eric.
This being could easily be thought of as more of a manifestation.
It seems to be a bringer of certain messages. Every time it has been seen in the movie, Eric learns/sees something that reveals more of his past to him, mainly about Alessa and her burning (similar to the special form of Demon Nurse in the movie, which is only seen when big/horrible events are about to happen). It also seems to be slightly helping Eric along, or at least watching him (similar to Valtiel from Silent Hill 3), as scenes in part 4 will show.
It does not attempt to harm Eric.