Peel ginger and halve crosswise. Cut pieces lengthwise into 1/16-inch-thick slices, then cut slices into 1/8-inch-wide julienne strips and transfer to a 2-quart heavy saucepan.
Remove zest from 3 oranges in long wide strips with a vegetable peeler, removing any white pith from zest with a paring knife, and add to ginger in pan. Fill pan three-fourths full with cold water and bring to a boil. Boil 1 minute, then drain in a sieve. Return zest and ginger to pan and refill with cold water. Bring to a boil, then reduce heat and simmer, uncovered, 10 minutes. Drain zest and ginger. Repeat simmering with more cold water for another 10 minutes, then drain.
Bring 1 1/2 cups water, 1 cup sugar, and salt to a boil in saucepan, stirring until sugar is dissolved. Add zest and ginger and gently simmer, uncovered, stirring occasionally, until zest and ginger are completely translucent and syrup is thickened, 15 to 20 minutes. Drain candied zest and ginger in a sieve, discarding syrup.
Meanwhile, cut 1/2 inch from top and bottom of all oranges with a sharp knife, exposing fruit at both ends. Cut peel and pith from sides (leaving no white parts) with paring knife, trimming fruit if large (but retaining orange shape) to 2 1/2 to 2 3/4 inches wide at middle. Discard trimmings.
Bring wine, orange juice, 1/2 cup Grand Marnier, and remaining cup sugar to a boil in a deep 12-inch heavy skillet, stirring until sugar is dissolved, then boil 3 minutes. Add oranges, arranging in 1 layer, and simmer, covered with a tight-fitting lid, 10 minutes. Transfer oranges with a slotted spoon to a serving dish, inverting them (so syrup coats oranges). Add candied zest and ginger to syrup and boil over moderate heat, uncovered, until syrup is thickened and mixture is reduced to about 1 1/4 cups, 10 to 15 minutes. Remove from heat and stir in remaining 2 tablespoons Grand Marnier.
When oranges are cool enough to handle, cut each crosswise into thirds on a cutting board, then reassemble "whole" in serving dish. Spoon zest mixture, including syrup, over oranges, arranging zests and ginger decoratively over them. Chill oranges in serving dish until cold, at least 1 hour.
Just before serving, spoon syrup in dish over oranges to coat. Serve chilled or at room temperature.