By Herbert Lash

NEW YORK (Reuters) - The price of crude oil slid further on Tuesday, driving the dollar higher and spurring sharp gains in U.S. and European equities, especially oil-sensitive shares and the beaten-down financial sector.

A one-two punch of rising supply from the Organization of Petroleum Exporting Countries and declining U.S. demand pushed oil to a fresh three-month low of $118 a barrel in New York.

The slump in crude prices helped the dollar to a six-week high versus the euro, and euro zone government bonds rose in thin trade ahead of a Federal Reserve policymakers' meeting.

The Fed -- the U.S. central bank -- is expected to hold benchmark interest rates steady amid poor housing and credit market conditions, while signalling inflation concerns even as oil prices ease.

Facing the highest U.S. unemployment rate in four years and the lowest existing-home sales pace since early 1998, monetary policy-makers are expected to be more downbeat about the economy's outlook than they were at their June meeting.

U.S. Treasury debt prices slipped after a report on the service sector that was stronger than expected alleviated some fears about the depth of the U.S. economy's deterioration.

Investors snapped up shares broadly, but particular strength was evident in energy-consuming sectors, including airlines and industrial companies. Shares of retailers, tech and financial services companies also gained.

General Electric (GE.N: Quote, Profile, Research) gained more than 3 percent and was the biggest boost to the broad S&P 500. Insurer American International Group (AIG.N: Quote, Profile, Research) rose nearly 8 percent to lead the Dow's climb, while on Nasdaq, the top boost was Apple Inc (AAPL.O: Quote, Profile, Research), up 2.7 percent.