Pour the oil in a large bowl and add the peppers, tomatoes, onion, squash, zucchini, and basil in a bowl and toss to combine. Season with salt and pepper, to taste. Let vegetables stand for 10 minutes before placing them into a BBQ wok basket.
Heat the grill to medium. Place vegetables (in the wok basket) on the grill and cook, stirring occasionally. Remove the vegetables from the grill and serve immediately.