Cook orzo according to package directions; drain. Rinse with cold water; drain again. Transfer pasta to a large bowl. Cover; chill in the refrigerator for 1 to 2 hours. Add feta, tomatoes, olives, basil, and parsley to the chilled pasta; stir to combine.
In a jar with a screw-top lid, place olive oil, lemon juice, garlic, and oregano. Shake vigorously to combine. Pour dressing over pasta mixture; toss to coat. Season to taste with salt and ground black pepper. Cover; chill in the refrigerator for 2 to 24 hours.