I grew up on a poultry farm and we never had problems with possums - and there were possums in the woods near us. Most of our problems were with feral dogs and cats. Occasionally snakes but that was few and far between. I don't ever remember a possum coming into the hen house. But if they did, I'd expect them to go for the chicken feed, rather than the chickens. They're much more scavengers than killers.
I'd have to shoot the dogs and cats. They would just keep coming back. The dogs ran in packs but the cats would be solitary.
Mike