Combine the strawberries, rhubarb, and sugar in a large container. Cover and refrigerate overnight. Strain the liquid that has accumulated into a pitcher. Stir in the vinegars. Refrigerate until ready to use.
To make a cocktail, mix 1 shot of gin, white rum, or vodka and 1 1/2 shots shrub syrup in a 6 ounce glass. Top with club soda.