Heat olive oil in a large skillet over medium-high heat. Cook and stir sausage, mushrooms, onion, green bell pepper, and garlic in the hot oil until sausage is browned and crumbly, about 20 minutes; drain and discard grease.
Stir tomato sauce, diced tomatoes, tomato paste, and olives into sausage mixture; season with oregano, basil, and salt. Simmer mixture until flavors infuse, about 30 minutes.
Bring a large pot of lightly salted water to a boil. Cook spaghetti in the boiling water, stirring occasionally until cooked through but firm to the bite, about 12 minutes. Drain and transfer to a serving bowl; top with tomato-sausage sauce and Parmesan cheese.