Heat oil in large pot over medium-high heat. Add the onion and bell pepper and cook until beginning to soften, 3 to 5 minutes. Add garlic, bay leaves, oregano, white wine, water, clam juice, and tomatoes. Bring to a boil, reduce heat to medium, and simmer for 5 minutes. Season with salt and pepper, to taste.
Add the fish, mussels, shrimp and clams, in that order. Let cook, covered and undisturbed, until the clams and mussels have opened and the shrimp and fish are cooked through, 5 to 7 minutes. Remove the lid and garnish with chopped parsley. Spoon into bowls and serve immediately while hot.