Heat grill. Shape ground beef into 4 (4-inch-square) patties.
When ready to grill, place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 13 to 15 minutes or until thoroughly cooked, turning once.
Meanwhile, brush onion slices with oil. Add onion to grill during last 5 to 8 minutes of cooking time; cook onions until tender, turning once. Prepare bread as directed on package for grill. Top each patty with cheese slice; cook just until melted.
To serve, place onion slice on each patty on grill. Spread 1 side of 4 slices of toast with salad dressing; spread remaining 4 slices of toast with steak sauce. Top each steak sauce-spread slice of toast with onion-topped patty. Cover each with salad dressing-spread slice of toast.