Mix together the orange juice, lemon juice, lime juice, salt, black pepper, thyme, garlic, ginger, chilli, curry powder, allspice, nutmeg and cinnamon in a bowl. Whisk in the vegetable oil.
Pour 3/4 of the marinade into a resealable plastic zipper bag and place the chicken wing pieces into the bag. Squeeze out any air, mix the wing pieces with the marinade and refrigerate from 4 to 12 hours. Place the remaining 1/4 of the marinade in a small bowl and refrigerate until grilling time.
Preheat barbecue for medium heat and lightly oil the grate.
Remove the wing pieces from the bag of marinade and discard the used marinade. Sprinkle the wings with salt and pepper to taste and sear on the hottest part of the grate until the wings begin to brown, about 4 minutes per side.
Move the wings to a less-hot part of the barbecue, baste with the unused portion of the marinade and close the lid. Cook until the wings are golden brown, show good grill marks, are no longer pink in the center and the juices run clear, 10 to 15 more minutes. Baste again with marinade and turn after 5 to 8 minutes.