In a large bowl, combine the vinegar, oil, sugar, 1 teaspoon salt, and 3/4 teaspoon pepper and stir until the sugar is dissolved. Add the cabbage, onion, and parsley and toss to combine.
Cut away the peel and white pith of the oranges. Slice the fruit into thin half-moons and gently fold into the cabbage. Refrigerate, covered, tossing occasionally, for 2 hours. Serve chilled or at room temperature.
To Bring It: The slaw can be made up to 2 days ahead. Just leave out the oranges, which lose their bright color over time. Pack them separately and fold them in just before serving.