In a food processor or blender, combine Feta cheese, Greek yogurt, red wine vinegar, minced garlic, black pepper and oregano well mixed and creamy.
In a medium sized bowl, combine cucumber, tomatoes, olives, onion and parsley. Season with a pinch of salt and pepper. Set aside.
Warm tortillas slightly in the microwave, just enough to make the pliable (about 15-20 seconds). Lay one tortilla on a flat surface and spread ¼ of the feta mixture evenly on the tortilla, leaving about 1/3 of an inch around the edges. Scoop 1/4 of the cucumber mixture onto the tortilla and spread evenly.
Roll tortilla into a log shape. Wrap tightly with plastic wrap. Repeat with the remaining ingredients, then refrigerate logs for at least 30 minutes or up to overnight.
When ready to serve, remove logs from the refrigerator. Unwrap and slice into even pieces using a sharp, serrated knife. Secure pinwheels with toothpicks if desired.
Arrange on a serving platter and garnish with fresh parsley, if desired.