In a large saucepan or Dutch oven brown half of the pork cubes in hot oil; remove meat and set aside. Brown the remaining meat with the onion and garlic. Return all of the meat to saucepan. Stir in the chicken broth, oregano, and cumin. Bring to boiling; reduce heat. Cover and simmer for 40 minutes.
Stir in the hominy and green chilies. Cover and simmer for 30 minutes more. Skim off fat. Ladle into bowls. If desired, serve with sliced radishes, shredded cabbage, and sliced green onion. Makes 6 to 8 main-dish servings.