Clean, wash and drain the strawberries well. Halve or quarter the fruits depending on size and put them into a bowl. Add sugar and vanilla sugar and mix in. Cover and chill for about 30 minutes.
Wash the mint and lemon balm, shake dry, pluck leaves from the stalks and, except for a few for garnishing, chop coarsely. Clean the rhubarb, wash and pat dry. Cut the stems into quarters and cut them into pieces of about 10 cm length.
Put strawberries, chopped mint and lemon balm in a large punch bowl. Add white wine and sparkling wine and pour rhubarb juice over it. Garnish with the remaining mint and lemon balm. Arrange punch in glasses and garnish with a rhubarb stick.