Place strawberry layer ingredients in a food processor or blender. Blend until completely smooth. Spoon strawberry puree evenly into popsicle molds, filling each one ⅓ full. Freeze 30 minutes.
In a small bowl, whisk yogurt layer ingredients until smooth. Spoon over frozen strawberry layer, filling another ⅓ full. Freeze 30 minutes, then insert a popsicle stick in the middle of each mold.
Place blueberry layer ingredients in a food processor or blender. Blend until completely smooth. Spoon evenly over yogurt layer. Freeze popsicles until completely firm, about 1 hour.