Cook the pasta according to package directions until al dente. Drain well using a colander and rinse with cold water to stop the cooking process and prevent sticking. Transfer the cooled pasta to a large mixing bowl.
While the pasta is cooking, prepare the vegetables. Halve the cherry tomatoes, dice the cucumber and bell pepper, finely chop the red onion, and slice the black olives. Add these to the bowl with the pasta.
Crumble the feta cheese over the pasta and vegetable mixture. Add the chopped fresh parsley and dill (if using) to the bowl.
In a separate small bowl or jar, whisk together the olive oil, red wine vinegar, lemon juice, Dijon mustard, minced garlic, and dried oregano. Season generously with salt and freshly ground black pepper. Whisk until well combined and emulsified.
Pour the dressing over the pasta salad. Gently toss everything together until all the ingredients are evenly coated with the dressing. Be careful not to overmix, which can make the pasta mushy.
For best flavor, cover the bowl and refrigerate for at least 30 minutes (or up to several hours) to allow the flavors to meld before serving. This step is crucial for a truly delicious pasta salad.