Cook the spaghetti according to package instructions until al dente. Drain and rinse under cold water to cool.
In a large mixing bowl, combine the cooled spaghetti, cherry tomatoes, cucumber, bell pepper, red onion, black olives, mozzarella balls, and Parmesan cheese.
In a small bowl, whisk together the Italian dressing, dried oregano, salt, and pepper.
Pour the dressing over the salad mixture and toss gently to combine.
Cover the salad and refrigerate for at least 30 minutes to allow the flavors to meld.
Serve chilled or at room temperature.