Bring a large pot of salted water to a boil. Cook pasta according to package instructions until al dente. Drain and rinse under cold water to cool.
While the pasta cools, prepare the vegetables: halve the cherry tomatoes, chop the cucumber, and slice the red onion. Soak the red onion in water for 5 minutes to reduce its sharpness. Drain and pat dry.
In a large bowl, combine the cooked pasta, cherry tomatoes, artichoke hearts, cucumber, and drained red onion.
In a separate small bowl, whisk together olive oil, lemon juice, garlic, dill, oregano, salt, and pepper. Stir in the feta cheese until well incorporated, creating a creamy dressing.
Pour the dressing over the pasta and vegetable mixture. Gently toss until everything is well coated. Taste and adjust seasoning if needed.
Chill in the refrigerator for at least 30 minutes before serving to let the flavors meld. Serve cold or at room temperature.