In the bowl of a slow cooker, combine the sausage, chicken, onion, celery, bell peppers, garlic, tomatoes, chicken broth, Cajun seasoning, and oregano.
Cover, and cook for 3-4 hours on low.
Add the rice. Stir, cover, and cook another 1-2 hours, or until rice is cooked.
Stir in the shrimp, and cook an additional 20-30 minutes, or until shrimp is cooked through. Serve with fresh parsley.