Make soup: Rinse squid under cold running water and pat dry.
If squid are large, halve ring of tentacles, then cut longer tentacles crosswise into 2-inch pieces.
Pull off flaps from squid bodies and cut into 1/4-inch-thick slices. Cut bodies crosswise into 1/4-inch-thick rings.
Pat shrimp dry and sprinkle with pepper and 1/4 teaspoon salt.
Heat oil in a wide 6- to 8-quart heavy pot over moderately high heat until hot but not smoking, then sear shrimp in 2 batches, turning over once, until golden but not cooked through, about 2 minutes per batch.
Transfer shrimp with a slotted spoon to a bowl.
Add garlic, red pepper flakes, and oregano to pot and sauté, stirring, until golden, about 30 seconds.
Add wine and 1/2 cup water and bring to a boil. Stir in clams and cook, covered, over moderately high heat until shells open wide, checking frequently after 6 minutes and transferring as opened with a slotted spoon to bowl with shrimp. (Discard any unopened clams after 8 minutes.)
Stir in mussels and cook, covered, over moderately high heat until shells open wide, checking frequently after 3 minutes and transferring as opened with a slotted spoon to bowl with shrimp. (Discard any unopened mussels after 6 minutes.)
Put oven rack in middle position and preheat oven to 425°F
Add stock to pot along with remaining 4 cups water, tomatoes with juice, sugar, and remaining 1/2 teaspoon salt and simmer, uncovered, 15 minutes.
Make toasts while stock simmers: Arrange bread slices in 1 layer on a baking sheet, then drizzle with oil and season with salt.
Bake, turning over once, until golden, about 10 minutes total. Transfer toasts to a rack to cool slightly, then rub lightly with cut sides of garlic and sprinkle with parsley.
Finish soup: Add halibut to stock and cook at a bare simmer, covered, until just cooked through, about 2 minutes.
Stir in squid and reserved shellfish, then remove from heat and let stand, covered, 1 minute. Stir in basil and parsley and serve immediately, with toasts alongside for dipping.