Bring a large pot of salted water to a boil.
Cook the orzo according to the package directions until al dente.
Drain and rinse under cold water to cool completely.
In a small bowl, whisk together the olive oil, lemon juice, red wine vinegar, Dijon mustard, oregano, garlic, salt, and pepper.
In a large mixing bowl, combine the cooled orzo, cucumber, cherry tomatoes, feta cheese, olives, red onion, and parsley.
Pour the dressing over the salad and toss gently until everything is evenly coated.
Refrigerate for at least 30 minutes before serving for the best flavor.
Serve chilled.