Preheat oven to 350º. In a large, deep skillet over medium-high heat, brown ground beef with diced onion until meat is done through. Drain off any excess fat. Add in each of the 3 soups, green chilies, & enchilada sauce. Over low heat, allow to simmer for 5 minutes. In a greased 9 x 13 baking dish, arrange 6 tortillas in bottom of pan in a single layer. Add 1/3 of meat mixture & top with 1/3 of the cheese. Continue with layers of tortillas, meat mixture & then cheese until all ingredients are used. Bake uncovered for 30 - 40 minutes til hot through.