Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente, then drain and rinse briefly under cold water to stop cooking.
While pasta cooks, whisk together olive oil, lemon juice, minced garlic, dried oregano, salt, and pepper in a small bowl to make the dressing.
In a large mixing bowl, combine the cooked pasta with half of the dressing while still warm. Toss well to coat.
Add halved cherry tomatoes, diced cucumber, sliced red onion, halved Kalamata olives, crumbled feta cheese, chopped parsley, and chopped mint to the bowl.
Pour remaining dressing over the salad and gently toss everything together until evenly combined.
Let the salad rest at room temperature for at least 15 minutes before serving to allow flavors to meld. Taste and adjust seasoning with more salt or pepper if needed.