For additional mint flavor, freeze chopped mint leaves with water in ice-cube trays to make flavored cubes.
Stir together mint and 2 cups hot water; let stand 25 to 30 minutes. Pour through a wire-mesh strainer into a 2-quart container, discarding mint.
Stir in sugar and next 3 ingredients. Chill 8 hours. Pour mixture into a large punch bowl. Stir in strawberries and remaining ingredients just before serving. Serve over ice.