Cook penne in salted boiling water according to package directions until al dente. Drain and rinse under cold water.
Whisk together olive oil, red wine vinegar, lemon juice, Dijon mustard, oregano, garlic powder, salt, pepper, and sugar in a small bowl.
Dice the cucumber, onion, and bell pepper. Halve the cherry tomatoes and slice the olives.
In a large bowl, combine the cooled pasta, tomatoes, cucumber, onion, bell pepper, olives, mozzarella, and parsley.
Pour the dressing over the salad and toss to coat evenly. Add the Parmesan and toss again.
Refrigerate for at least 30 minutes before serving, then toss once more and serve.