NEW YORK—Wall Street scored a moderate gain after a volatile session Wednesday that saw the major indexes ratchet up and down on the seesawing price of oil and mixed feelings about the financial sector.

Concerns about mortgage financiers Fannie Mae and Freddie Mac initially dragged down financials. Wall Street is nervous that the government-chartered companies will need a bailout from the Treasury Department, a move that could wipe out shareholders’ equity. Fannie Mae shares tumbled nearly 27 percent, while Freddie Mac shares lost 22 percent.

Oil prices finished higher—...