Of all the advocacy groups that have trekked to Capitol Hill to appeal for help, the one that appeared in the hearing room of the House Merchant Marine Committee yesterday was one of the most improbable: Greek shipping tycoons.

In a presentation to members of Congress, staff aides, maritime lobbyists and representatives of maritime unions, the Union of Greek Shipowners painted a grim picture of a depressed merchant fleet, starved for cargo and scrapping vessels because of the worldwide recession.

A "sustained, unprecedented shipping slump" and a "sustained decline in freight rates since 1980" have resulted in "an incredible number of ships laid up," according to Costa Carras, spokesman for the group.

The Greeks, who operate more merchant ships than any other nation, have been hit disproportionately hard by plummeting worldwide trade, he said. When added to a drop in oil-tanker demand that goes back to the 1974 oil crisis, the shipping slump has forced nearly all vessels in the vast Greek-owned fleet to operate at a loss, Carras said.

What has happened to the Greeks appears to be the inevitable outcome of a worldwide recession in which trade between industrialized nations declined, and of the financial crisis afflicting Third World nations, whose imports have dropped as slumping demand for their exports eroded their hard-currency resources.

According to statistics compiled by several sources, the volume of world seaborne trade declined 7 percent last year, after a 5 percent drop in 1981. More than 1,500 ships have been mothballed, and oil tankers totalling 25 million deadweight tons of capacity were sold for scrap in 1982. Freight rates for the cargo that is moving are about 5 percent lower than in 1976.

The slump has affected Greek owners three ways. They own more than 12 percent of all merchant ships in the noncommunist world, they committed themselves to expansion at a time of record high interest rates, and their own small nation has relatively little international trade of its own, which means the Greeks must compete to carry cargo between third countries that are increasingly protectionist-minded.

Carras said the condition of the Greek fleet is important to the United States because it is "one of the prime assets available to NATO in the event of a general war."

Rep. Sam Gibbons (D-Fla.), a veteran advocate of free trade, asked, "What is it you want us to do?"

Both Carras and Aristomenis M. Karageorgis, president of the Union of Greek Shipowners, said they were not seeking any direct aide from the U.S. government.

But they did ask for support from Congress and the maritime industry for their efforts to keep world shipping routes open to "cross-traders" such as the Greek fleet.

Carras said the United States should drop its bilateral cargo-sharing arrangements with Brazil and Argentina--an unlikely occurrence, according to industry sources--and should forego implementation of new agreements with the Philippines and Venezuela.

He also said that the United States should support Greece's attempt to weaken a wordwide shipping code adopted by the U.N. Conference on Trade and Development that would guarantee Third World fleets a greater share of international cargo. He called for rejection of a cargo-preference bill sponsored by Rep. Lindy Boggs (D-La.), aimed at increasing the minuscule share of this nation's bulk cargo carried by American-registered vessels.