Peel and section oranges over a bowl; squeeze membranes to extract juice. Set sections aside; reserve 1 1/2 tablespoons juice. Discard membranes.
Cut beets into wedges.
Combine reserved 1 1/2 tablespoons juice, vinegar, oil, salt, and pepper in a medium bowl; stir well with a whisk.
Divide beet wedges and orange sections evenly among 6 salad plates. Top each serving with 2 tablespoons onion slices. Drizzle with vinaigrette, and garnish with pomegranate seeds, if desired.
Note: To obtain pomegranate seeds, put on gloves and cut the pomegranate into quarters. Coax seeds out from the base with thumbs, being careful not to break seeds. Remove and discard white membrane. Reserve 1/3 cup seeds for garnish.