Place a large skillet over medium heat; cook the ground beef, onion, celery, and green bell pepper in the hot skillet until the beef is completely browned, 7 to 10 minutes. Sprinkle the oats, 3/4 teaspoon salt, the garlic powder, and 1/8 teaspoon black pepper into the beef mixture. Arrange the cabbage wedges atop the beef mixture.
Stir the tomato sauce, cider vinegar, and brown sugar together in a bowl; season with salt and pepper. Pour over the cabbage and beef mixture. Place a cover on the skillet and simmer until the cabbage is tender, 15 to 20 minutes.