Cook pasta according to package directions.
While the pasta is cooking, stir together the Greek yogurt, garlic, lemon juice, red wine vinegar, dill, and oregano in a large bowl.
When the pasta is done cooking, drain and run cold water over the pasta. Drain completely and drizzle with olive oil. Toss until pasta is well coated. Pour the pasta into the large bowl with the Greek yogurt mixture. Add the tomatoes, cucumber, olives, red onion, and feta cheese. Stir gently until ingredients are well coated. Season with salt and black pepper, to taste. You can add a little extra dill and lemon juice, if desired. Serve.
Note-if you need the recipe to be gluten-free, use gluten-free pasta. The pasta salad will keep in the refrigerator for up to 2 days.