Place hominy in a large Dutch oven. Cover with water to 4 inches above hominy; cover and let stand 8 hours. Drain. Return hominy to pan. Cover with water to 4 inches above hominy; bring to a boil. Reduce heat, and simmer 1 hour, stirring occasionally; drain. Wipe pan dry with a paper towel.

Heat oil in pan over medium-high heat. Add pork to pan; sauté 5 minutes, turning to brown on all sides. Add onion; sauté 2 minutes or until tender. Add oregano, salt, garlic, and bay leaf; sauté 1 minute. Return hominy to pan. Add 3 cups water and broth; bring to a boil. Reduce heat, and simmer 30 minutes, stirring occasionally. Add chiles; simmer 30 minutes, stirring occasionally. Discard chiles and bay leaf. Ladle about 1 1/2 cups posole into each of 8 bowls. Garnish each serving with 1/4 cup cabbage, about 2 teaspoons cilantro, about 2 teaspoons radishes, about 2 teaspoons green onions, and 1 lime wedge.