Preheat the barbecue to medium-high heat. Lightly brush the nectarine pieces with vegetable oil and place on the grill over direct heat. Cook for 2 to 3 minutes on each side, or until browned and soft.
Remove the nectarines and dice them. Place the salad greens, grape tomatoes and red onion in a large salad bowl. Place the nectarines on top.
Whisk together the olive oil, vinegar, garlic, sugar and salt. Drizzle over the salad. Serve as is or toss to evenly coat with dressing. Serve right away.