Ezeulu has a fraught relationship with his sons; his family could reasonably be said to be dysfunctional. His son Edogo resents the fact that his father favors his brother Nwafo, whom he believes is being groomed for the priesthood. Edogo doesn't want to be chief priest himself, but he still smarts at his father's special treatment of Nwofo.
As for Obika, he doesn't have much of a relationship with his father to speak of. A juvenile delinquent who's always getting into mischief, he causes no end of trouble for his old man, who has no compunction in seeing him publicly whipped by the colonial authorities for his various transgressions against the law. There's a possibility of some reconciliation by the end of the story, but it's tragically cut short as Obika, with his newfound wisdom and respect for the old traditions, drops dead during a funeral ritual.
Then there's Oduche, Ezeulu's second youngest son. Although Oduche looks up to his father, Ezeulu manipulates his son, effectively making him a spy in the world of the white man by sending him to church and school. Ezeulu's motives in this regard are entirely selfish; he wants to gain as much knowledge of the white man as possible without compromising his position as chief priest. However, Ezeulu's plan backfires in spectacular fashion when Oduche becomes a militant Christian committed to destroying the worship of Ulu and all other pagan deities.