In large pot of boiling salted water, cover and cook potatoes until tender, 25 to 30 minutes. With slotted spoon, remove and let cool; peel and cut into 3/4-inch cubes. Place in large bowl.
Meanwhile, blanch leeks and celery in same boiling water for 20 seconds; drain in colander. Chill under cold water; drain well and add to potatoes.
In small bowl, whisk together mayonnaise, parsley, oil, lemon juice, salt and pepper; pour over vegetables and mix well. Sprinkle with feta cheese and olives.