Heat oil in a medium skillet over medium high heat, and cook chicken until no longer pink and juices run clear. Stir in sausage, and cook until evenly browned. Drain chicken and sausage, and set aside.
In a large, heavy saucepan over medium heat, blend olive oil and flour to create a roux. Stir constantly until browned and bubbly. Mix in garlic, and cook about 1 minute.
Gradually stir chicken broth and beer into the roux mixture. Bring to a boil, and mix in celery, tomatoes, sweet onion, diced tomatoes with green chile peppers, red chile peppers, parsley, and Cajun seasoning. Reduce heat, cover, and simmer about 40 minutes, stirring often.
Mix chicken, sausage, and shrimp into the broth mixture. Cook, stirring frequently, about 20 minutes.