The primary theme in "Oliver Twist" is the age-old battle between good and evil. As quoted in Enotes, Dickens once wrote that he "wished to show, in little Oliver, the principle of good surviving through every adverse circumstance, and triumphing at last". To this end, the characters in the story tend to be rather single-dimensional, with a few exceptions, they are either very good or very bad. Characters like Oliver, Mr. Brownlow, and the Maylies are virtuous, and those like Fagin, Monks, and Sikes are evil.
A second theme in the book is the effect of British laws during the first half of the 1800s on the poor. Reasoning that the enactment of "Poor Laws" would save much money on the care of the indigent, the government confined those mired in poverty in workhouses, where they were starved and mistreated with no avenue of redemption. These laws paradoxically resulted in the development of a seedy underground of crime, and rates of lawlessness soared.
Alienation is another theme that the story explores in depth. Each of the characters are alienated both from each other and society. As an orphan, Oliver is the stereotypical outcast, and, with the possible exception of Dick, the people in his life are only out for themselves. Although the good people in the story do share moments of community and trust, their numbers are small, and they are far outnumbered by their unscrupulous counterparts.
For a much more comprehensive discussion on themes, check out the second Enotes link below. Good luck!