In a small skillet over medium low heat, combine oil, butter and garlic. Cook garlic in butter and oil gently for 2 or 3 minutes. Remove garlic butter mixture from heat.
Place a large nonstick skillet on the stove over medium high heat. Using a pastry brush, brush 1 side of 4 slices of bread with garlic oil and place buttered side down in skillet. Top each slice with equal amounts of the 4 cheeses, distributing them equally over the 4 slices. Top each sandwich with another slice of bread brushed with garlic butter, buttered side up. Flip the grill cheese sandwiches a few times until cheeses are melted and gooey and bread is toasty and golden. Cut grilled 4 cheese sandwiches from corner to corner and serve.