Boil balsamic vinegar about 12 minutes or until syrupy and reduced to 1/4 cup; set aside.
Meanwhile, combine sugar and water in a small saucepan; bring to a boil, stirring constantly. Boil 30 seconds, remove from heat, and let cool 5 minutes.
Purée the strawberries and sugar syrup in blender.
Fill 10 pop molds halfway with the strawberry purée; freeze 1 hour or until somewhat firm. Top with the balsamic reduction, pour in the remaining strawberry purée, and add the pop sticks; freeze 3 hours or until firm.