Combine the chicken, mushroom and chicken soups. Add the chopped onions, and sour cream or milk. Stir in the green chilies. Preheat the oven to 325 degrees. Grease a 9-inch by 13-inch pan and spread the tortilla strips in the bottom of the pan. Spread the sauce over the tortilla strips and sprinkle the cheese on top. Bake covered for about 60 minutes and then remove the cover and bake 15 more minutes uncovered. Serve with tortilla chips, sour cream, and salsa.