Oedon is a Great One without form. Interestingly, Oedon has a tomb in the game, implying it has died. The Yharnam Stone says: "The Queen lies dead, but her horrific consciousness is only asleep, and it stirs in unsettling motions." and the Isz Chalice implies the Great Ones are able to function on transcendental planes of thought. It seems possible if not likely that Oedon may have died, but continues to exist on a different plane of thought. Perhaps death simply takes the Great Ones to a different plane in the first place.
This video explains a possible interpretation of Oedon: