If the sin offering was offered to cover the sins of the anointed priest (Lev 4:3) then the priest wasn't free to eat ANY part of the animal. God got His part, but the rest of the animal - including its head and entrails - were burnt outside the camp (Lev 4:11).
But if the sin offering was offered for the common people, it seems as though the rules changed. The Lord still received His part (the blood, fat, kidneys and fatty lobe above the liver etc) but the priests were free to eat the remainder of the animal (Lev 6: 26). However, does this mean they were free to eat EVERYTHING including the entrails (e.g. stomach, tongue and liver etc) or was he only free to eat the muscle meat?
I assume he was free to eat even the entrails because back in Leviticus chapter 4, the entrails were part and parcel of the 'remainder' of the animals.