Heat the vegetable oil in a large saucepan over medium heat. Stir in the garlic, onion, bell pepper, and celery. Cook and stir until the onion is translucent and the celery is tender, about 10 minutes. Stir in the tomato sauce, chopped tomatoes with their juice, and diced tomatoes; season to taste with salt and pepper. Bring to a boil over medium-high heat; reduce heat and simmer 30 minutes.
Stir in the crawfish tails, and simmer until hot, 5 to 10 minutes.
