In a 3- to 4-quart pan over high heat, frequently stir celery and onion in oil until lightly browned, about 5 minutes. Add yams, apples, and broth; bring to a boil, cover, reduce heat, and simmer until yams are tender when pierced, about 15 minutes.
With a slotted spoon, transfer vegetables and apples to a blender or food processor; whirl until smooth, adding enough cooking liquid to purée easily. Pour purée back into pan and stir over medium-high heat just until steaming, 2 to 3 minutes.
Ladle soup into wide bowls. Add yogurt, salt, and pepper to taste.