Preheat oven to 350°.
Trim fat from pork; sprinkle pork with black pepper. Pour 1 cup water into a shallow roasting pan. Place pork on a rack coated with cooking spray; place rack in pan. Bake at 350° for 1 hour and 15 minutes or until tender. Remove pork from bones; reserve bones. Shred meat into bite-size pieces. Discard drippings.
Combine 10 cups water, chicken, 1 cup onion, salt, bay leaves, and garlic in a stockpot; bring to a boil. Reduce heat; simmer 1 hour. Remove from heat. Remove chicken from broth. Place chicken in a bowl; cool 15 minutes. Strain broth through a sieve into a bowl; discard solids. Remove chicken from bones; discard skin and reserve bones. Shred meat into bite-size pieces. Return broth, pork bones, and chicken bones to pan. Bring to a boil; cook until stock is reduced to 6 cups (about 20 minutes). Strain stock through a sieve into a bowl; discard solids. Place a large zip-top plastic bag inside a 2-quart glass measure. Pour broth into bag; let stand 10 minutes (fat will rise to the top). Seal bag; snip off 1 bottom corner of bag. Drain broth into pan; stop before fat layer reaches opening. Discard fat. Add pork, chicken, kale, and hominy; bring to a boil. Reduce heat; simmer 5 minutes.
Ladle posole into each of 6 bowls. Top each with 1 tablespoon oregano, 1 tablespoon onion, and 1 lime piece. Serve with warm tortillas, and sprinkle with crushed red pepper, if desired.