Rinse goose inside and out with cold water. Dry the goose and cut away any large fat layers in the body cavity. Remove stray pinfeathers. Fasten neck skin to back with skewer.
Put goose in a large soup pot and cover with ginger ale. Simmer gently, uncovered, for 30 minutes, until fat rises to top. Drain off fat and ginger ale, add fresh ginger ale to cover, and simmer 30 minutes longer.
Preheat oven to 325 ° F. Remove goose from ginger ale and dry with paper towels.
Spoon the stuffing into the body cavity, packing it lightly.
Truss goose and put it on a rack in a shallow roasting pan. Roast 3-3 1/2 hours (16 minutes per pound), until drumstick meat is soft to the touch and joint moves easily. Spoon off fat as it accumulates. Do not prick skin and be sure not to overcook goose. After 1 hour of roasting, cover any places getting overly brown with orange slices.
To prepare the garnish, cut long strips of peel from the oranges, using a vegetable peeler or sharp knife. Arrange the strips in coils around the goose, and tuck celery leaves or parsley into the coils. Do not serve the wings; they have no meat.