Cook the cheese tortellini according to package instructions. Drain and rinse under cold water to cool.
In a large mixing bowl, combine the cooled tortellini, cherry tomatoes, cucumber, red bell pepper, red onion, black olives, feta cheese, and fresh basil.
In a small bowl, whisk together the olive oil, red wine vinegar, dried oregano, salt, and pepper.
Pour the dressing over the pasta salad and toss gently to combine.
Cover and refrigerate for at least 30 minutes to allow flavors to meld.
Serve chilled or at room temperature.