Help with varmint trouble?

ive have been having problems with an animal(s?). whatever it is has killed two of my chickens, my dad found one mangled corpse behind our small chicken coop without the head. what possibly could have done this, and how do i catch it? weve also had problems with something taking the lid off our chicken food container and getting in the food, how should i trap this animal? my uncle caught one young racoon in a pressure plate trap and disposed of it, but that only ended our problems for a little bit.