Light 1 side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Dry each wing well with paper towels. Toss together wings and oil in a large bowl. Sprinkle with salt and pepper, and toss to coat.
Place chicken over unlit side of grill, and grill, covered with grill lid, 15 minutes on each side. Transfer chicken to lit side of grill, and grill, without grill lid, 10 to 12 minutes or until skin is crispy and lightly charred, turning every 2 to 3 minutes. Toss wings immediately with desired sauce. Let stand, tossing occasionally, 5 minutes before serving.