Combine the orange juice, lemonade, and pineapple juice and stir well.
Bring 3 cups water and the sugar to a boil in a heavy saucepan and boil until sugar is dissolved, about 5 minutes. Let cool. Add the syrup to the fruit juices.
Place the whole strawberries into a ring mold. Pour in enough fruit juice to fill the mold. Freeze. Refrigerate the remaining juice.
When ready to serve, pour the fruit juice into a punch bowl and add the soda. Float the strawberry ice ring in the punch.