Scrub potatoes and cover with cold salted water in a saucepan. Bring to a boil; reduce the heat and simmer, covered; for about 15 minutes, until potatoes are tender.
Meanwhile whisk the oil, with the vinegar, oregano, salt and pepper. Drain the potatoes and slice while warm. Add the red onion and gently toss with the dressing.
Divide greens between 4 plates. Top each one with an equal amount of with warm potato salad.