Several major oil companies and small, West Coast producers are pressing exports of California crude oil to Japan and other countries, including possibly Mexico.

Their problem is the oil now arriving at West Coast ports from Alaska. Without exports, this increased supply is threatening to undercut prices, producers fear.

One California producer, Everett (Red) Hodges, president of Century Oil Co., has already filed two export applications with the Commerce Department to sell up to 25,000 barrels of oil a day to Japan.

Commerce is holding the application pending a recommendation from the Energy Department Energy Secretary James R. Schlesinger is said to favor exports as one possible solution to the supply-price problem on the coast.

But approval of oil exports would be a ticklish thing for the administration. The United States now has to import about 8 million barrels of oil a day. This has put the U.S. balance of trade and the balance of payments into steady deficit and helped drive down the value of the dollar, which in turn has added to inflation at home and caused problems with trading partners abroad.

The administration's entire energy plan, embodied in legislation stalled on Capitol Hill, is aimed at reducing oil imports.

Century Oil's Hodges want to swap his oil with the Japanese for foreign oil to be delivered later to other points in the United States.

But other producers simply want to sell to foreign buyers, without swaps.

James Woods, head of the California Independent Producers Association, said, "All the West Coast refining companies, and major oil companies, with our support, favor exports of crude and refined products. They are under the gun the most."

The major oil companies involved include California-based Union Oil. Atlantic Richfield (Arco) and the Standard Oil Co. of California. Arco also is a major producer of oil on Alaska's North Slope, and has a substantial share in the $10 billion Alaskan oil pipeline.

President Carter last summer over-turned Schlesinger's preference for allowing sales or swaps of Alaskan oil to Japan. Carter ruled out such transaction in July because the administration expected Congress would act to bar them in legislation that cleared the way for construction of the 800-mile trans-Alaska Pipeline.

Energy Department officials are optimistic, however, that California crude oil and refined products do not carry what one senior officials described as "the stigma of Alaskan oil."

Another official, Edward Mampe, said the department can probably allow the sales without going to Congress for approval.

In addition to Japan, department officials and oil industry executives say that Korea, Taiwan, and Mexico are also potential buyers of California oil, or refined products. One reason these countries are interested in the sales, they say, is that they do not have stringent air quality regulations that make the high-sulfur California crude oil more expensive to refine for U.S. markets.

California is the third largest oil-producing state in the country, providing about 1 million barrels of oil a day for domestic markets.

West Coast oil inventories are bulging as a result of increased shipments from Alaska's North Slope, which went into production last June.

Woods said California refiners now have nearly 16 million barrels of residual oil and other products in clogged inventories, more than twice the amount they had last year. These supplies are expected to increase even more as Alaskan production rises.

The Alaskan output is expected to increase 400,000 barrels a day by April, to a total of 1.2 million barrels daily.

The Energy Department's Economic Regulatory Administration published proposed ruling in the Federal Register this week on ways to deal with the California supply-price problem. These alternatives include exports.

"Sales or swaps to countries like Japan might be the way to get something going rather quickly," says David J. Bardin, head of the regulatory group.

The main alternative would be to make changes in the so-called entitlements program, under which the department regulates the price of various kinds of domestic crude oil.

These changes would make California crude more attractive to refiners, and cause the companies producing Alaskan oil to ship more of it through the Panama Canal to Gulf Coast or Eastern refineries. That, too, would relieve the California producers, but would be very complicated, federal experts say.

Bardin said the department will hold hearings on these alternatives in California later this month, and that he expects a decision by mid-summer.