Combine strawberries with 2 tablespoons of corn syrup and 1 tablespoon of sugar in a blender OR food processor and puree until smooth. Transfer to a small bowl and set aside.
Combine yogurt with remaining 2 tablespoons of corn syrup and 2 tablespoons of sugar in another bowl. Add vanilla and stir until smooth.
Spoon mixtures into popsicle molds in alternating layers. Swirl layers using a thin knife to pull the berry mixtures up the sides creating fun designs. Add sticks and freeze until solid; about 12 hours or overnight. To unmold popsicles, run water along the sides until loosened.