Process first 8 ingredients in a blender until smooth, stopping to scrape down sides.
Cut jícama into cubes, or, if desired, cut into 1/4-inch-thick slices, then cut with a 1 1/2-inch star-shaped cutter.
Place jícama, salad greens, strawberries, cranberries, and, if desired, orange sections in a large bowl. Drizzle with vinaigrette, and gently toss to coat. Garnish, if desired.
NOTE: For testing purposes only, we used Ocean Spray Cran-Fruit Crushed Fruit For Chicken (Cranberry Orange flavor) for the cranberry-orange relish. Look for it near the cranberry sauces in your grocery store.