Boil the pasta in salted water as per package instructions until al dente, about 8 minutes. Drain and let cool slightly.
In a large bowl, whisk together lemon juice and zest, red wine vinegar, minced garlic, oregano, and a pinch of salt and pepper. Gradually add the olive oil, whisking continuously.
Add the cooked pasta, cucumber, bell pepper, cherry tomatoes, shallots, parsley, capers, and olives to the dressing. Toss until well coated. Gently fold in the feta cheese.
Cover the salad and refrigerate to let flavors blend, at least 30 minutes, or up to 24 hours. Toss again before serving. Enjoy chilled or at room temperature.