Finely grate 1 tsp. zest from one of the oranges and put in a large bowl. Using a sharp knife, trim off the peel and white pith from the oranges and cut crosswise 1/4 inch thick.
Squeeze two or three orange slices over a small bowl to yield 1 Tbs. juice; add the juice to the zest along with the olive oil, onion, and vinegar. Whisk to blend and season to taste with salt and pepper. Arrange the remaining orange slices and the avocado slices to one side of 6 salad plates.
Toss the mâche with the dressing, season to taste with salt and pepper, and mound next to the oranges and avocados.