In a small bowl, combine the cheese, garlic powder, oregano and cayenne; set aside. In a small saucepan, heat butter and oil until butter is melted. Coat two-thirds of each pretzel rod with butter mixture, then roll in cheese mixture. Reheat butter mixture if needed.
Place in an ungreased 15x10x1-in. baking pan. Bake at 275° for 20-25 minutes or until golden brown, turning once. Cool. Store in an airtight container.