One of Sohio's top Washington lobbyists modestly describes his oil company: "We're one of the big little guys."

Standard Oil of Ohio has grown at a breakneck pace from $800 million in assets less than a decade ago to $6 billion today. Now it also has a king-sized problem and is being watched anxiously by the British government, Wall Street, the Middle Eastern oil producers, the oil industry, some of the nation's largest pension funds, and Jimmy Carter.

The reason is on the cover of Sohio's recent annual report - the Trans-Alaska Pipeline.

Sohio is at the center of a situation that Carter's top energy adviser, James R. Schlesinger Jr., says poses "political problems, and problems in symbolism."

The problem is what to do with an estimated 500,000-barrel-a-day oil "surplus" on the West Coast once oil starts flowing at full capacity through the 800-mile Alaskan pipeline later this year.

Most of that surplus oil is Sohio's.

One would expect government energy planners and oil company executives to be delighted to have "surplus oil" during an energy crisis. But this one confronts them with prickly political and economic questions.

Carter has three basic options.

he can hold surplus oil in the ground. He can allow the oil companies to export it for sale to Japan. Or he can have the companies absorb high transportation costs shipping the oil to Gulf Coast markets.

"If you decide to keep the surplus Alaskan oil in the ground, you are making a decision which hurts me because it will kill my company," warned Charles E. Spahr. Sohio's chairman, last December.

This threat, financial analysts say, would send a chill to creditors who have lent billions to Sohio. These include some of the nation's largest banks, and investors such as Connecticut General Life Insurance Co., and the Ohio State Teachers Pension Fund.

"The financial community not only has an interest in having that oil flow, but having it flow at the highest possible price," says William Randall, a Wall Street oil analyst with F. Eberstadt and Co.

Another key player is British Petroleum, which is owned in part by the British government, and bought into Sohio to help it finance its share in the pipeline. BP now holds 26 per cent interest in Sohio. Through a complicated financial arrangement that interest increases to over half once Sohio achieves maximum production.

While British government officials have not lobbied hard on Carter's Alaskan oil decision, they have expressed continuing interest. Anthony Wedgewood Benn, the energy minister, met with administration officials earlier this year.

"He talked like BP had before on the need to create incentives to have people continue drilling," said one Federal Energy Administration official.

She second option, allowing exports to Japan, is the most controversial.

"It would be the most felicitous of all worlds for the companies," says FEA Administrator John F. O'Leary.

Privately the companies admit that if they can export the oil to Japan at world prices they will make up to a dollar or more per barrel from lower transportation costs.

Among the other players who favor Japan exports:

The state of California, because of the threat of added pollution.

The state of Alaska, which would receive higher income under a comlicated taxing formula if the oil goes to Japan rather than to the lower 48 states.

West Coast oil producers and marketers, such as Standard Oil of California, who fear that "discounted" Alaskan oil would force down profit margins in a bloated market.

While Schlesinger, according to administration sources, continues to favor "swapping" Alaskan oil shipments to U.S. Gulf Coast ports, the companies suspect Carter will not be able to sell it politically.

Consequently, the companies are scrambling to ensure that as much of the West Coast surplus as possible is sopped up in a way that will not depress oil prices on the West Coast.

Socal, one of California's largest producers and marketers, is negotiating to take up to 250,000 barrels a day of Alaskan oil from Sohio, and smaller amount from Exxon, another of the Alaskan oil producers. In exchange Socal will "back out" as oil men say, Saudi Arabian crude oil, bound to Sohio's partner, BP, for use in other markets.

Sohio has also contracted tankers to carry crude oil to the Gulf Coast if Carter does not approve sales to Japan.

"It is not a question of disaster. We and the other companies have made provisions to move the bulk of the surplus by the end of the year." says Frank E. Mosier. Sohio's senior vice president for marketing and refining.

To reduce the likelihood of "soft" West Coast oil market, Carter has reversed a previous Ford administration pledge to maximize production from the Elk Hills Naval Petroleum Reserve.

He is also weighing an increase above the 1 billion barrels in the Strategic Petroleum Reserve.

One Library of Congress energy analyst says. "The administration has a vested interest in maintaining price in real terms . . . the President's program depends very heavily on higher prices."

What may be good for Sohio or even good for the nation in some respects could be hard to sell on Capital Hill, however. One oil analyst warned:

"Congress loves cheap prices. If you keep Alaskan crude in U.S. markets, you will drive down prices."

That would be bad for Sohio and all the other interested parties.