U.S. allies in Europe and Japan are hoping that anticipated Republican losses in this Tuesday's mid-term congressional elections will cause the Reagan administration to soften its right-wing orthodoxy and pursue more conciliatory policies in economic and defense matters.

Governments in West Germany, France, Italy and Japan are known to feel that a mild Republican defeat could have salubrious effects on the Atlantic Alliance, especially if the White House is encouraged to seek lower interest rates and lift sanctions against firms involved in building the Soviet-European gas pipeline.

At the same time, the allies fear that a sweeping Democratic victory poses risks of a power stalemate in Washington for the next two years that would handicap the strong U.S. leadership needed to pull the West out of recession and relieve antagonisms with the Eastern Bloc.

A survey of Washington Post correspondents showed that while Tuesday's elections have not stirred a great deal of public interest abroad, governments will be looking at the results as a referendum on Reagan's stewardship in the White House and as a harbinger of possible policy shifts.

Bonn officials credit the elections with prodding the administration toward a compromise on the pipeline controversy, chiefly because sanctions have caused some layoffs at U.S. firms in key congressional districts.

Unless a deal is struck by election day, some allied officials are worried that pressures on Reagan to resolve the conflict will dissipate and momentum toward a settlement will be lost.

"The sanctions decision does not help the president in his domestic politics," observed a West German official. "I can imagine that the administration is interested in achieving a solution before the elections to help some candidates."

On the other hand, the administration may feel more inclined to offer tangible concessions only after the election campaign is over -- primarily to avoid charges that it caved in to European demands.

In Moscow, the coming U.S. vote has evoked unprecedented scrutiny among officials eager to discern the future course of Reagan's policies. A task force composed of specialists from numerous think tanks has been assembled to study Tuesday's election results.

The Soviets believe that if the Republicans drop fewer than 20 seats in the House of Representatives, the White House will probably reaffirm its tough line against detente. A loss of more than 20 seats, however, could presage the collapse of the working coalition between House Republicans and conservative Democrats that Moscow perceives as Reagan's power base.

Polish officials also are closely monitoring the election for signs of weakness in Reagan's stature, which they hope will lead to a softening of sanctions imposed when the independent trade union Solidarity was suppressed by martial law.

A Polish expert on U.S. affairs, Prof. Longin Pastusiak, was quoted in a Warsaw newspaper as predicting that "the Republicans will have to pay in the coming elections . . . and President Reagan will have to revise his internal and foreign policies and switch to a moderate line."

In Peking, disillusionment with Washington over a range of issues, from Taiwan arms sales to the defection of a Chinese tennis star, has grown so strong that all talk of a strategic partnership against the Soviets has ceased.

Diplomats believe that one motive for China's resumption of a political dialogue with the Kremlin for the first time in three years stemmed from a conviction that prospects for good relations with the Reagan administration seem virtually nil.

U.S. restrictions on high technology trade also have irked the Chinese. On a trip to New York recently, Foreign Minister Huang Hua said, "One cannot help asking: does the U.S. government regard China as a friend or an adversary?"

Chinese suspicions toward the Reagan administration were reinforced by the appointment of George P. Shultz to be secretary of state. Shultz is considered sympathetic to Taiwan because of previous business contacts there.

In the Middle East, Israel and neighboring Arab countries are watching the election outcome to determine its impact on Reagan's ability to press ahead with his peace initiative, which calls for a Palestinian homeland on the West Bank in confederation with Jordan.

Preoccupied with the aftermath of its invasion of Lebanon, Israel seems to be less absorbed than usual by the 1982 U.S. elections.

Nonetheless, Israeli officials are keenly observing races involving staunch congressional supporters of Israel, such as Senators Henry M. Jackson (D-Wash.), Daniel Patrick Moynihan (D-N.Y.) and Howard M. Metzenbaum (D-Ohio), to see if American public opinion has shifted against them.

More than ever, Arab countries now appear to perceive Washington as their sole hope in restraining Israel. Moderate leaders have tried to improve relations with Reagan by praising the "positive aspects" of his peace proposal and renouncing plans to seek the expulsion of Israel from the United Nations after the U.S. voiced strong objections.

Egypt, in particular, hopes that the elections will vindicate Reagan's leadership and encourage him to confront the perplexing conflicts that have eroded progress toward a comprehensive Middle East peace since the Camp David accords were signed.

Developing countries in Latin America, Asia and Africa have not evinced much interest in the elections, but analysts there remain concerned about the decline in U.S. foreign aid and lack of emphasis that Washington currently attaches to Third World problems.

Like the Europeans, impoverished countries see the mid-term vote as a referendum on Reaganomics and hope that a blow to the Republicans will elicit a new trend toward lower interest rates and reflation of the U.S. economy that might boost world trade and improve their beleaguered state.

Some developing countries quarrel with specific thrusts of Reagan's foreign policy, especially in cases where U.S. strategic considerations have buttressed traditional enemies.

India sharply opposed U.S. policy in South Asia because Reagan has funnelled aid to its ancient foe--Pakistan--in order to thwart Soviet expansionism.

U.S. military and economic aid to Pakistan has been tripled to more than $500 million for the coming fiscal year, while American food and development assistance to India has dropped to $210 million.

The Reagan administration's early efforts to improve ties with Argentina collapsed when it supported Britain during the war over the Falkland Islands. Other Latin American nations also were chagrined by the U.S. decision to back London.

A more persistent complaint, however, is that Washington seems more concerned with guerrilla activity in Central America than with planning long-term relief for the hemisphere's shell-shocked economies.

Huge debts brought Mexico and Brazil, two of Latin America's most influential countries, to the brink of bankruptcy earlier this year. Latin American countries use 60 percent of export income to service debts.

The deep-rooted dissatisfaction felt in the region was emphasized two weeks ago when Latin American representatives of the Inter-American Development Bank met in Rio de Janeiro and criticized U.S. contributions scheduled for the next three years as inadequate.