Skewering the onion slices through all the layers ensures ease of grilling and keeps pieces of onion from falling through the grill.
Soak wooden skewers 20 to 30 minutes. Heat a grill to medium. Skewer the white and red onion slices, passing the skewer through each layer; skewer the green, red, orange, and yellow peppers. Place the skewered vegetables, olive oil, salt, and pepper in a shallow bowl, and turn the vegetables until they are coated.
Place vegetables on grill, and cook until lightly charred, 6 to 8 minutes per side. Transfer vegetables to a cutting board. Cut peppers into 1/2-inch-thick slices, and remove skewers from onions. Transfer vegetables to a serving platter.