Combine chicken, salt, pepper, and 2 quarts water in a large stock pot; bring to a boil. Reduce heat; simmer, uncovered, 1 1/2 hours or until chicken is tender.
Remove chicken from broth; cool slightly. Remove meat from bones, discarding bones. Coarsely chop meat; set aside. Set broth aside in stockpot.
Sauté onion in oil in a large skillet until tender. Remove onion with a slotted spoon, and drain well, reserving oil in skillet. Set onion aside.
Dredge beef and veal in flour; brown meat in reserved oil. Drain well.
Add reserved chicken, sautéed onion, and browned meat to broth; add 2 quarts water. Bring to a boil. Reduce heat; simmer, uncovered, 4 hours, stirring occasionally.
Stir in tomatoes, corn, lima beans, peas, garlic powder, paprika, angostura bitters, and remaining water; continue to simmer, uncovered, 1 hour, stirring occasionally.
Ladle stew into individual serving bowls; serve warm.