The Many-Angled Ones (aka, Lloigor) exist in a space that contains more dimensions than our universe therefore they appear to humans as "many angled." Therefore when one of them manifests in our universe, it appears to us as the floating disconnected body parts of a larger creature. Unlike the entities of the Cthulhu Mythos, the goal of the many-angled ones is to impose on the multiverse a rigid geometrical order thereby making everything run like clockwork.
No matter what host body a Many-Angled One takes, it possesses superhuman strength, reflexes, and speed. It's extremely durable and nearly invulnerable. From the eyes it incredibly destructive beams. Regardless of whether, they stole a body or specifically built it to host their lifeforce, they appear to always have these powers.