Heat a 6 quart heavy stockpot and add the oil, onion, and garlic. Saute until they are clear, about 5 minutes. Add the remaining ingredients, except the seafood, and simmer, uncovered, until the sauce is rich and full-flavored, about 1/2 hour.
Add the fish and shellfish in the order given, giving each variety a moment to cook. The clams will take longer than the squid.