Place the celery, diced onion, peppers, and garlic in a large stockpot. Turn the heat to high, stir, and cook until the vegetables give up their liquid and are tender, about 8 to 9 minutes. If the vegetables start to stick, add the olive oil. Season with salt and pepper.
Add the fennel and bay leaves, sauté for 1 minute, add the stock and potatoes, and bring to a boil. Skim and simmer, stirring occasionally, for 5 minutes or until the potatoes are about half-cooked (test by removing a slice and cutting it). Add the tomatoes, stir, and simmer for about 7 minutes.
Add fish fillets and shrimp, stir, and simmer for about 1½ minutes, or until the seafood looks halfway cooked. Stir in the oysters and herbs. Cook for about 1 minute, until the edges of the oysters curl. Add the crabmeat, stir, simmer, and adjust seasoning. Turn off heat.
Serve in large bowls, and sprinkle with green onions.