Following are some of the major activities on this week's agenda for the White House and Capitol Hill. WHITE HOUSE

President Carter makes a two-day visit to U.N. headquarters in New York this week, his first visit as chief executive to the international organization. He is to address the General Assembly Tuesday morning sign two international convenants, host two working lunches and a working dinner for heads of delegations, and in between, confer with Secretary General Kurt Waldheim and other world leaders.

The President's U.N. trip highlights the week's White House calendar which also includes two big legislative campaigns, the beginning of a nationwide health service education program and renewed emphasis on the nation's economy, now showing encouraging signs after the doldrums of the past two months.

Carter's U.N. visit - following two weeks of talks with Israeli and Arab officials and last week's meetings with Soviet Foreign Minister Andrei Gromyko - can be expected to include discussions of a Middle East settlement and a hoped-for extension of the U.S.-Russian arms limitation pact which expires today. It is believed Carter also will bring up questions of both hunger and human rights around the world. continued U.S. foreign aid was brought up last week by Treasury Secretary W. Michael Blumenthal in an address to the annual meeting of the World Bank and International Monetary Fund. The United Nations would be the logical international forum for Carter to advise financially stable nations they must assume more of the burden of assisting poorer countries.

The two big legislative campaigns on tap for the week center around the Carter energy package and a program to put people back to work. Constant liaison between the White House and the Capitol will be in effect as Congress moves toward deciding on the energy plan - the President's No. 1 legislative goal this year. Also cranking up will be a drive in behalf of the long pending Humphrey-Hawkins bill, described as a "full employment" measure. Concurrently, big labor is launching an all-out champaign for the so-called Labor Law Reform Act and can be expected to ask the White House for help. A bill to revise the National Labor Relations Act is to be called up in the House Tuesday.

Health, Education and Welfare Secretary Joseph A. Califano Jr. will kick off a nationwide education campaign Tuesday in behalf of a national health program. Califano is to preside at a hearing here, the first of more than 100 hearings to be held throughout the nation to explain administration thinking and solicit public recommendations on the health program which is to be sent to Congress early next year.

On the economic front, Carter will be looking at new tax reform proposals, ideas to stimulate business interest, more jobs to increase consumer purchasing power and measures to cut back increases in the nation's trade deficit.

On tax reform, it appears that the President is sending his tax writers back to their drawing boards. Blumenthal acknowledged last week that the administration's tax overhaul package will not be ready for at least several more weeks.

On another front, Carter revealed that he will be in touch with the House and Senate Democratic leadership on "wasteful" spending programs of the Pentagon. Funds taken out of the military pipeline would be used for such economic recovery programs as public works and jobs-producing programs.

The big trade deficit that was announced last week will be the subject of talks between the President and Commerce Secretary Juanita Kreps, who is returning from a trade trip to Asia.

Two important economic reports are to be issued next week and will be given careful scrutiny by Carter and his top economic aides. They are the wholesale price report, to be released Thursday, and the monthly employment report, coming out on Friday.

Also on tap for Friday is a speech by Carter at the conclusion of a two-day meeting of the Democratic National Committee. The session will follow Thursday meetings of the DNC Executive Committee, its finance group and various caucuses, including those representing blacks and women.

Vietnam will figure in this week's White House calendar. The remains of 22 Americans who died during the Vietnam war were released by Hanoi last week. A bill related to the Indochina was probably will be signed by the President this week. It is a $69 billion money measure providing funds for the Department of Housing and Urband Development and several of the government's independent agencies, including the Veterans Adminstration. CAPITOL HILL

It could be a big week for organized labor in Congress, but the filibustering Senate is expected to prevent a double labor celebration.

Bills to improve the lot of the American workers are pending in the House and the Senate. The House has scheduled its measure - the Labor Reform Act - for Tuesday. The labor bill pending in the Senate would increase the minimum wage. But action will be put off as the Senate struggles with its filibuster. When the talkative senators might run out of gas in filibustering the natural gas bill was anybody's guess. Efforts to cut off the filibuster will continue under prodding from the leadership of both parties and the White House which is anxious to get the Carter energy program started.

While the Senate talks, the House will be acting on eight or more bills. Today's program includes federal trade Commission amendments and a locks and dams bill. Labor law overhaul is slated for Tuesday, supplemental appropriations and cargo-preference legislation on Wednesday, and the bank audit bill and Marine Mammal Protection Act on Thursday. On Friday the House will begin a four-day recess to observe Columbus day.

Congressional committees have announced full schedules for this week, but Senate panels may be curtailed by early and late sessions as a result of their filibuster.

Hearings on Social Security financial are to continue before the Senate Finance and House Ways and Means committees. A house Labor subcommittee as scheduled hearings on private pension plans, while military retirement systems will be taken up by a House Armed Services subcommittee. The question of legal services for the elderly will be examined by the Senate Human Resources Committee.

Energy bills other than natural gas pricing are to come up at various Senate committee meetings . Department of Energy nominations will be considered by the Energy and Natural Resources Committee today, deep-sea mining on Tuesday. Oil Cargo preference legislation will be before a joint Energy-Commerce subcommittee on Wednesday.

The Senate Foreign Relations Committee begins the second of three weeks of hearings on the Paname Canal treaties Tuesday, with members of Congress as witnesses. A house International Relations subcommittee will meet Tuesday to discuss withdrawal of troops from South Korea and a House Judiciary subcommittee, on Thursday, will consider treaties with Mexico and Canada providing for a transfer of prisoners.

Other committees will be meeting on broadcast agreements for the 1980 Olympic Games, the needs of the federal aid highway programs, the adequacy of civil defense preparations and ways to make it easier to purchase homes.