Add the onion, celery, bell pepper, garlic, sausage, and chicken to the slow cooker. Pour in the canned tomatoes and sprinkle the oregano, bay leaves, and Creole seasoning over the top. Stir everything gently so the flavors start blending together.
Cover the slow cooker and set it to HIGH for about 3 hours (or LOW for 4–5 hours). During this time, the vegetables soften, the chicken cooks through, and the spices meld beautifully into the tomato broth.
After the main cooking time, stir in the thawed shrimp and the rice. Cover again and cook until the rice absorbs the liquid and the shrimp turn pink and tender — usually 20–30 minutes. Remove bay leaves before serving.