I have found little consistent in how animal parts used as food are named. How can I correctly refer to the tongue of ducks, the necks of ducks, or the ears of pigs?
Do you like duck's neck?
Do you like duck necks?
Do you like ducks' necks?
Is there a way which is most "correct" or formal?
As you yourself note, it is animal parts, not *animals’ parts. That’s because we use the creature’s name as an attributive noun not as a possessive one.
People therefore eat duck eggs, crab claws, shark fins, lobster tail, fish heads, frog legs, hog jowls, pig lips, rabbit shanks, calf testicles, whale blubber, dog legs, salmon roe, turkey breasts, lamb loin, ox tail, goose liver, beef shoulder, monkey brains, and chicken hearts.
They do not eat *ducks’ eggs, *crabs’ claws, *sharks’ fins, *lobsters’ tails, *fishes’ heads, *frogs’ legs, *pigs’ lips, *hogs’ jowls, *rabbits’ shanks, *calves’ testicles, *whales’ blubber, *dogs’ legs, *salmons’ roe, *turkeys’ breasts, *lambs’ loins, *oxen’s tails, *geese’s liver, *beeves’ shoulders, *monkeys’ brains, or *chickens’ hearts.
Going by how dishes are referred to in other languages, I would treat the animal parts as a dish name in this instance. Duck's neck is the name of the dish, regardless of how many ducks died to make it. To refer to several necks belonging to several ducks is closer to veterinarian medicine.
So in a conversation, or at a restaurant, you might be asked "Would you like some duck's neck?" the same way you would be asked whether you would like some pork. The pork might be made up of several pigs, but in French - which is where the dish name comes from - they would not refer to it as "porcs" (pigs).
So the dish name would be singular. Duck's neck, cow's tongue, etc. If there are several dishes, for several people, then you might say "Two servings of duck's neck."
