Special equipment: A vegetable spiral slicer
Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper. Combine the onion and enough salted water to cover in a small bowl; let soak about 15 minutes.
Meanwhile, place the potato spirals on the prepared baking sheet; drizzle with oil and sprinkle generously with salt and pepper. Roast until just cooked through, about 10 minutes.
In another small bowl, whisk together the lemon juice, vinegar and oregano. Whisking constantly, stream in the 2 tablespoons oil until combined; season with salt and pepper.
Drain the onion. Place the potato spirals in a serving bowl. Add the tomatoes, olives, cucumber and onion and toss. Sprinkle with feta and oregano.