It is problematic when we want to trace word origins as it leads us to an old word that just has us wondering where that one originated. Tower of Babel, I suppose. That being said, here is what the OED says:
chicken comes from the Middle Dutch kiekijn.
lamb comes from the old English l�mb, which is said to relate to the old words in several European languages.
Beef comes from the French b�uf which in turn came from the Latin bov-em.
Pork comes from the Latin porc-us which means swine, hog.
I have no idea how helpful that is, but cest le vie.