Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until cooked through but firm to the bite, about 13 minutes. Drain.

Heat vegetable oil in a skillet over medium heat; cook and stir onion and garlic until onion is tender, about 5 minutes. Add zucchini, yellow squash, bell peppers, and mushrooms; continue cooking and stirring until vegetables are tender, about 5 minutes more. Pour tomatoes into skillet and season with oregano, basil, red pepper flakes, salt, and black pepper; bring to a simmer.

Cook shrimp in vegetables sauce until they are bright pink on the outside and the meat is no longer transparent in the center, about 5 minutes. Serve shrimp and sauce over rigatoni.