NEW YORK—Wall Street finished sharply higher Tuesday as oil prices dropped for the second straight day and investors were encouraged by the possibility of more help for the ailing financial system. The Dow Jones industrials gained more than 150 points, and all the major indexes were up more than 1 percent.

Crude prices tumbled $5.33 to settle at $136.04 a barrel on the New York Mercantile Exchange, bringing oil’s two-day drop to more than $9. Other commodities also pulled back.

Speeches by Federal Reserve Chairman Ben Bernanke, Treasury Secretary Henry Paulson and JPMor...