Wash oxtails to remove any bone fragments and place in a large bowl. Cover oxtails with cold water and weigh down with a plate to keep them submerged. Place in the refrigerator for 12 hours, changing the water 3 or 4 times. Drain.
Combine drained oxtails and stew meat in a large pot with fresh water to cover. Bring to a boil and cook about 10 minutes. Drain and rinse meat. Return parboiled meat to the large pot and add onions and water to cover, approximately 3 times the volume of meat. Bring to a boil and cook for 3 hours. Reduce to a low simmer and cook 3 hours more.
Skim fat and onions from the top of the soup. Place soup in the refrigerator to cool until you can skim additional fat from the surface, about 2 hours.
Reheat soup over medium heat until hot, about 5 minutes. Season soup with leeks, salt, and pepper.