Some of this country's largest corporations could lose billions of dollars in overseas sales because Congress, rushing to get out of town two weeks ago, failed to provide new funding for the Export-Import Bank which has run out of lending authority.

The companies affected include such household names as Boeing, General Electric, Westinghouse and Lockheed.

They have turned for help to influential senators, including particularly Appropriations Committee Chairman Warren G. Magnuson, in whose home state of Washington Boeing is based.

Congress may yet come to the rescue, but in the meantime the companies are stranded.

The Ex-Im money ran into multiple problems on that getaway night two weeks ago.

First, it came up this year as always as part of the foreign aid money bill, which Congress doesn't like and almost always puts off.

Second, it came up against the new congressional budget process, where limits on spending forced Congress to choose between foreign aid and domestic aid to the states in the form of revenue sharing. Revenue sharing won hands down.

It all happened as House and Senate raced to pass a supplemental appropriations bill to tide over various overspent agencies for the rest of the fiscal year ending Sept. 30. The Senate had foreign aid money in its version; the House did not. They went to conference and the House agreed to put a little foreign aid money in, taking it from revenue sharing. Then someone remembered that revenue sharing is an entitlement program and it is illegal not to give it all out. So the House went back to its original position, the Senate yielded -- after many speeches -- and the Ex-Im Bank and its clients were out in the cold.

The Ex-Im Bank makes loans at moderate interest rates to foreign customrms who buy U.S. products; it is designed to stimulate exports. This fiscal year's existing authority of $3.75 billion is all used up.

Griff Ellison, vice president for public affairs, said Congress' failure to act is blocking immediate sales totaling about $300 million and an added $2.6 billion a littlle farther down the road. Through the end of fiscal 1981, on Sept. 30, 1981, U.S. firms could sell up to $8.3 billion in goods overseas with the help of Ex-Im financing, Ellison said. If it isn't forthcoming, foreign competitors could grab these contracts, and "hundreds of thousands of jobs" could be lost to U.S. workers, he said.

Thus, on the night of July 2 and in the few days before as the dispute over the funds unfolded, Capitol Hill was swarming with lobbyists for companies like G.E., Boeing, Bethlelhem Steel, GTE, Westinghouse and General Motors and "probably all the major companies in the United States," according to a congressional aide.

When they lost, there were bitter words from such senators as Magnuson, whose Boeing could lose up to $800 million in the next year, Republican Jake Garn of Utah ("There is no more money left in the till to finance the sale of American products overseas"), Jacob K. Javits (R-n.y.), Daniel K. Knouye (D-Hawaii) and several others.

Former ambassador and assistant secretary of state Dwight Porter, now with Westinghouse, said in a phone interview yesterday that his company is bidding on contracts to build four reactors in Korea, a $2 billion deal, in competition with the French and wouldn't have a chance without Ex-Im Bank financing.

It is also competing with the Germans and French on Taiwan reactors, worth $1 billion, in which the other bidders already have given guarantees similar to Ex-Im financing. The Korean and Taiwan jobs "are right on our platter, and down the road we and Allis-Chalmers are bidding on a big hydro job in Argentina-Paraguay at close to $1 billion," he said.

A General Electric spokesman said the company sells gas turbines, locomotives and jet engines overseas and is deeply concerned. "A lot of it goes under Ex-Im financing," he said. A Lockheed spokesman said, "We're selling airplanes overseas all the time and a lot of the foreign sales are funded by Ex-Im Banks."