Heat the vegetable oil in a skillet over medium heat. Add the onion, bell pepper, and celery; cook for about 4 to 5 minutes, stirring constantly. Add the garlic and cook for 1 minute longer.
Stir the remaining ingredients into the vegetable mixture and turn the heat to low. Simmer, uncovered, for about 15 minutes.
Add shrimp and sausage or serve with chicken or fish fillets.