Pour the orange soda, orange juice concentrate, barbecue sauce, brown sugar, and teriyaki sauce into a bowl, and stir to combine and dissolve the sugar.
Preheat oven to 350 degrees F (175 degrees C). Remove any excess pieces of fat from inside the duckling, place the duck into a roasting pan, and prick the skin all over with a fork to allow the fat to drain off while roasting.
Brush the duckling with the orange mixture. Place the mushrooms into the cavity of the duck, and spoon in some of the orange sauce.
Roast the duck in the preheated oven, brushing it every 20 to 30 minutes with the orange sauce, until a meat thermometer inserted into a thick part of a thigh reads 165 degrees F (75 degrees C), about 2 1/2 hours.