Heat the oven to 425°F (220°C). Line a large rimmed sheet pan with parchment. Toss the potatoes with 2 teaspoons of the oil, half the salt, pepper, paprika, and garlic powder. Spread cut-side down and roast for 15 minutes.
Toss the sausage, peppers, and onion with the remaining oil, salt, and oregano. Turn the potatoes, add the sausage mixture, and spread everything in one layer.
Roast 18–22 minutes, turning once, until the potatoes are fork-tender with browned edges and the sausage is hot. Use two pans if crowded so the vegetables roast instead of steam.
Drizzle with red wine vinegar, scatter parsley over the pan, and serve hot. Refrigerate leftovers within 2 hours.