Preheat grill. Brush both sides of the onion slices with olive oil and season with salt and pepper to taste. Grill on each side for 2 to 3 minutes. Just to obtain grill marks and cook slightly. Remove from grill and coarsely chop. Combine onions in a medium bowl with cucumber, oregano and toss with the yogurt-mint dressing. Season with salt and pepper to taste. Sprinkle with feta cheese.
Whisk all ingredients together in a medium bowl and season with salt and pepper, to taste. Serve immediately.