It is hard to boil down all of the conflict in Oliver Twist to one main thread, even though all conflict in the novel essentially centers around young Oliver's fate. Though Oliver is mostly a passive character himself, possession of Oliver is desired by most of the characters. His half-brother Monks wants him out of the way so he can rob the boy of his inheritance. Mr. Brownlow and Rose Maylie want to give Oliver a loving home. Fagin wants to turn the innocent Oliver into a hardened criminal. A repentant Nancy wants to save Oliver from a life on the streets by risking her own safety to do so. Oliver himself figures little in any of these conflicts: in fact, he spends the book unaware of Monks's plotting against him.
Ultimately, it might be best to identify the main conflict of the novel as Oliver and his allies versus society, even if Oliver himself is a relatively reactive character. Oliver's society treats him as vermin, because he is an orphan born to an unwed mother. It is presumed that he will become a criminal, so no compassion is offered to him.
Fagin in particular is committed to transforming the guileless child into a criminal by forcing him to participate in illegal activities, thus
slowly instilling into his soul the poison which he hoped would blacken it, and change its hue for ever.
However, kind benefactors such as Mr. Brownlow and redeemed criminals like Nancy come to the boy's aid, allowing him to triumph over his circumstances.