Put a baking sheet in the oven and preheat to 475 degrees F. Toss the potatoes with 2 tablespoons olive oil, 1/2 teaspoon salt and a few grinds of pepper. Spread out on the hot baking sheet and roast, flipping halfway through, until browned and tender, about 25 minutes.
Meanwhile, make 3 shallow cuts in the fat on the side of the pork chops to prevent curling. Rub the pork with 3/4 teaspoon oregano and season with salt and pepper. Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add the pork and cook until just cooked through, 2 to 3 minutes per side. Remove to a large plate.
Add the tomatoes, garlic and remaining 1/4 teaspoon oregano to the skillet. Cook, stirring, until the tomatoes soften, about 2 minutes. Add the wine and cook until mostly dry, 1 to 2 minutes. Add 1/4 cup water and cook, lightly crushing the tomatoes, until slightly thickened, 1 to 2 minutes. Stir in the olives, sugar and any juices from the plate of pork; season with salt and pepper.
When the potatoes are done, sprinkle with the feta and let soften for a minute. Sprinkle with the dill and gently toss. Divide the potatoes and pork among plates. Spoon the tomato sauce over the pork and drizzle with the remaining 1 tablespoon olive oil.