In a medium skillet over medium, heat oil and add flour to make a roux. Whisking constantly, cook roux until it turns a chocolate brown color. Lower heat as necessary to keep from burning. This will take about 15 minutes.
Stir in celery, green pepper and onion. Cook 1 to 2 minutes. Add garlic and cook another 2 minutes. Transfer mixture to slow cooker crock.
Add chicken broth, tomatoes, Creole seasoning, chicken, sausage and okra to slow cooker.
Cover and cook on HIGH for 3 ½ to 4 hours or LOW for 6 ½ to 7 hours. Stir in shrimp. Cook just until shrimp is cooked through.