In a large pitcher, combine the tart cherry juice, vodka, orange liqueur, and simple syrup. Pour some of the mixture over ice and top it with sparkling water. To make the lychee garnish, in the center of each lychee, pipe some of the strawberry jam. Place a blueberry into the center of each lychee. Repeat until all of the lychees have been filled. Skewer two lychees on each toothpick and garnish the putrid punch. Serve immediately.