Cook orzo in salted water until al dente. Drain and rinse under cold water. Toss with olive oil and cool completely.
In a large bowl, combine cherry tomatoes, cucumber, red onion, parsley, and olives.
In a small bowl, whisk olive oil, lemon juice, lemon zest, Dijon mustard, garlic, salt, pepper, and oregano until well combined.
Add cooled orzo to vegetables and mix gently.
Pour dressing over salad and toss to coat evenly.
Add crumbled feta and gently fold in.
Chill for at least 30 minutes before serving.