Place the onion slices and feta cheese in a bowl, along with the parsley or green pepper if desired.
Mix together the oil, vinegar, lemon juice, oregano, salt, and pepper.
Add to onion and cheese, and allow to marinate for 2 or 3 hours before serving.
You may need a pinch of sugar if the dressing is too tart for your taste.
This is a great side dish for practically any meal.