The International Trade Commission yesterday found that heavyweight Japanese motorcycles have flooded the American market to the extent that the domestic industry needs protection, vividly demonstrating to visiting Prime Minister Yasuhiro Nakasone the extent of trade tensions between the United States and Japan.

The ITC will recommend to President Reagan next Wednesday whether the United States should impose tariffs on the large Japanese motorcycles or restrict their importation.

The ITC ruling by a two-to-one vote came just moments before Nakasone held separate meetings on Capitol Hill with congressmen and senators who are among the most vocal critics of Japanese trade policies and who are expected again this year to sponsor strongly protectionist legislation designed to restrict Japanese imports to this country.

"Compared to the shower of criticism I met yesterday I expect to find a storm today," the well-briefed Nakasone told members of the House of Representatives at a tea given by Majority Whip Thomas S. Foley (D-Wash.).

Foley said congressmen spoke "directly and candidly" to Nakasone, who expressed his determination to do everything he could to remove trade barriers within the limits placed on a democratic leader by Japanese voters who oppose trade liberalization measures.

"I'm not sure he changed any minds," said Foley. "I think by what he said and by his manner he tended to reassure some of the members that there would be follow-up action" on already announced moves to ease trade barriers.

From there Nakasone crossed the Capitol for lunch with 17 senators, and, according to Sen. John C. Danforth (R-Mo.), the Japanese prime minister demonstrated his political acumen. "He made a lot of converts on the Hill. A lot of people viewed him as very forthcoming, particularly on defense," said Danforth, chairman of the Senate Finance Committee's trade subcommittee.

Nakasone, however, clashed during the closed-door luncheon with Sen. Jesse A. Helms (R-N.C.) over Japanese reductions in tariffs on U.S. tobacco. The prime minister was reported to have called Helms "misinformed" for passing on "unfounded rumors" that the Japanese made up for the tariff cuts by raising fees charged for distributing foreign cigarettes. Nakasone said he would not allow the tariff cuts to be circumvented and had ordered an official who tried to do so fired.

The ITC ruling on motorcycles, meanwhile, was greeted as "a tremendous help" by Vaughn Beals, chairman of Harley-Davidson, the only American company still making motorcycles and the firm that brought the trade complaint.

Harley-Davidson complained that large-scale Japanese imports severely cut its sales and profits, forced a delay in its six-year modernization program and caused the layoff of 1,600 employes--40 percent of its workforce. No figures were given on the number of Japanese imports.

If President Reagan agrees to impose tariffs or quotas, Beals said, "We will be in a position to compete head-to-head with the Japanese without any further protection."

He said he prefers tariff protection, but refused to say how much. Under law, the president can increase tariffs by 50 percent for five years to give a company injured by heavy imports a chance to get on its feet.

"Imported motorcycles are a substantial threat of serious injury to the domestic motorcycle industry," said ITC Chairman Alfred Eckes, who cast one of the two votes in favor of the Harley-Davidson petition. He was joined by Veronica A. Haggart, while Paula Stern found that the domestic industry was not harmed by imports.

Eckes said the commission investigation showed that "foreign producers have flooded the U.S. market with heavyweight motorcycles" to the point where there is more than a one-year stock waiting to be sold.

A list supplied by the ITC showed that the four largest sellers of motorcycles in the United States are Japanese firms--Honda, 298,000 cycles; Yamaha, 201,000; Kawasaki, 129,000, and Suzuki, 111,000--with Harley-Davidson a far-behind fifth with 41,000 cycles.

In the same vote, the ITC refused, 2-to-1, to support Harley-Davidson's petition claiming it was injured by imports of Japanese motorcycle engines and power train sub-assemblies.