Cook potatoes in boiling salted water until tender, about 20 minutes. Drain, cool and dice potatoes (do not peel).
Combine potatoes and onions in large bowl. Add mayonnaise and toss to coat. Season with salt and pepper. Whisk vinegar, oil and oregano to blend in small bowl. Season dressing with salt and pepper. (Potato mixture and dressing can be made 1 hour ahead. Cover separately and let stand at room temperature.)
Arrange lettuce leaves on platter. Mound potato mixture in center, then arrange tomatoes, cucumber, green pepper and olives decoratively around potatoes. Pour dressing over and serve.