Mix together beef, crackers, egg, and onion soup mix in a bowl; shape into about 50 1-inch balls.
Heat oil in a non-stick skillet over medium-high heat. Brown meatballs in hot oil, about 2 minutes per side.
Stir apple jelly and ketchup together in a large pot over medium-high heat; cook and stir until the jelly melts and the mixture is smooth. Stir the wine into the jelly mixture, add the meatballs, reduce heat to medium-low, and cook at a simmer until the meatballs are cooked through, about 25 minutes.