In a large, deep frying pan, heat 2 tablespoons oil over medium heat. Cook onion rings, stirring occasionally, until they have turned golden, about 20 minutes. Transfer onions to a bowl and set aside. Raise heat to medium high and add 1 tablespoon oil. Cook apples until they soften or begin to turn golden, about 10 minutes, turning occasionally. Transfer apple slices to a bowl and set aside.
Preheat oven to lowest temperature. Heat remaining oil in the same frying pan and place pork medallions flat on bottom of the pan (cook in batches if necessary). Sprinkle lightly with Worcestershire sauce and season with salt and pepper. Cook over medium-high heat until browned on both sides. Transfer to a warm oven.
Deglaze frying pan with vinegar. Cook mushrooms in butter over medium-high heat, stirring frequently, until they begin to turn golden brown. Add reserved onions and apples to reheat. Season with salt and pepper. Serve pork medallions with vegetable-apple medley on the side. Spoon any juices remaining in the pan over the meat.