Heat olive oil in a large pot over medium heat. Add onion, green bell pepper, celery, and carrot; cook and stir until softened, about 5 minutes. Add garlic; cook and stir until fragrant, about 1 minute. Season with oregano, basil, salt, and pepper.
Pour chicken broth into the pot; simmer until celery and carrot are soft, about 20 minutes. Pour in crushed tomatoes and white wine; simmer until flavors combine, about 10 minutes.
Stir swordfish into the pot; cook until easily flaked with a fork, about 10 minutes. Pour in clams with juices; simmer until heated through, about 5 minutes. Stir in cornstarch until stew thickens, 3 to 5 minutes.