The game itself has no lore pointing as to exactly what is possessing the Channelers.
However, it seems likely that the incorporeal culprits are the Pokemon the Channelers are using to fight. It is already known that some Pokemon don't like being under a Trainer's control. It's a safe assumption that the Gastlies don't like being captured either, and are "lashing out" at the Channelers whose very job is to channel spirits.
Similarly, another possible theory is that it's no particular Pokemon (or it's the Marowak Ghost in the tower). Either way, these Pokemon Spirits are/were riled up due to the recent influx of Team Rocket and their message of evil[citation-needed]. Alternatively, the Spirits could be protesting the treatment of kindly Mr. Fuji, who was captured by Team Rocket. Again, these Spirits would go through the Channelers who already open themselves up to our etherial battling pets.
Although, both of the above answers are speculation and are just theories on the game. The game itself makes no direct reference to who/what the Channelers were possessed by, leaving it up to the Player to decide. Both possible explanations have their evidences and pitfalls, leading us to believe that there is no true answer.