Make dressing: Stir ingredients together in a bowl, seasoning to taste with salt.
Make salad: With a sharp knife, cut peel and outer white membrane from oranges, following curve of fruit. Slice oranges crosswise about 1/2 in. thick.
Cut avocados in half lengthwise, then pit and peel. Set each avocado half pitted-side down and slice lengthwise with cuts 1/2 in. apart. With a wide spatula, carefully transfer avocado halves to a platter (or individual plates) and press down gently to fan slices apart.
Arrange orange slices alongside avocados and top with watercress. Spoon about half of dressing over salad. Sprinkle nuts over salad and serve remaining dressing on the side.