Heat oil in a stockpot or Dutch oven over medium heat. Add onion and green pepper; cook, stirring, until softened, about 5 minutes. Add garlic and cook until aromatic, about 1 minute. Stir in wine and bring to a boil; cook for 3 minutes, then add tomatoes and their juice, clam juice, parsley, bay leaf, oregano and red-pepper flakes. Cover, leaving the lid slightly ajar; simmer, stirring occasionally, until the broth is rich and thick, 20 to 30 minutes.
Add mussels, cover and cook for 2 minutes. Remove the mussels with tongs as they open, reserving them in a large bowl. Discard any mussels that do not open. Add crab legs, return to a simmer and cook, uncovered, until the crab is heated through, about 5 minutes. Remove with tongs and reserve along with the mussels. Add shrimp, fish and chopped basil; cover and simmer until the shrimp turns pink and the fish is opaque, 2 to 3 minutes. Discard the bay leaf. Taste and adjust seasonings with salt and pepper. Return the reserved mussels and crab legs to the pot. Garnish with sprigs of fresh basil and serve.