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

A searching look at President Carter's legislative, foreign and political standings will be the order of the day.

Top strategists will be toting up the prospects for various Carter proposals with Congress and with world leaders, both allied and adversary. And at the end of the week, the President himself will embark on a three-day cross-country trip that will give him a good idea of how his nine-month-old administration is sitting with the voters.

First item on this week's pulse-taking by legislative aides will be the Carter energy program, the king-sized hang up on Capitol Hill. A routine of virtually continuous contact with congressional energy leaders will be in effect. Similar efforts in behalf of the Panama Canal treaties and government reorganization plans will continue.

New efforts also will be undertaken to draft a full employment program as originally outlined in the much-discussed Humphrey-Hawkins Bill.

Economic matters, including new analyses of what can be expected for the remainder of this year and in 1978, will occupy Carter's economic advisers. Problems in the nation's steel industry - and how the same issues of imports, jobs and production may affect other American industries - will be under study.

Three big government reports coming out this week also will be analyzed. They are the Federal Reserve Board's monthly report on industrial production, due today; the Commerce Department's update on the gross national product, to be released Wednesday, and the Labor Department's summary on how consumer prices are faring, coming out Friday.

Any serious change in the economic picture would be reflected in new thinking on revisions in individual and corporate taxes. Tax reforms, however, are now on a back burner until the new Congress in January.

Carter, assisted by Secretary of State Cyrus Vance and other top foreign advisers, will be concentrating on maintaining the momentum in the President's world peace crusades. New contacts with Israeli and Arab leaders will be sought, following Israel's response last week to new Middle East peace talks in Geneva. Talks with the Russians will continue in hopes of nailing down additional plants for Strategic Arms Limitation Talks.

The violence in Northern Ireland will be discussed when Roy Mason, Britain's secretary of state for Northern Ireland, meets today with Vance. A second foreign visitor will be Leo Tindemans. Belgium's prime minister who also is president of the European Council. Tindemans will meet Carter Wednesday and other U.S. officials on Thursday.

One cabinet member has just returned from an overseas mission, another will be leaving. Defense Secretary Harold Brown returned Saturday night from Europe and meetings at NATO headquarters in Brussels with U.S. and European military leaders. Leaving Friday will be Treasury Secretary W. Michael Blumenthal, on a two-week trip to Europe and the Middle East for conferences with finance ministers.

Carter's trip that will be a gauge of how the President's political fortunes are faring will begin Friday. He will go first to Detroit, to meet with urban poor; next to Omaha for a look at the headquarters of the Strategic Air Command; on to Des Moines for a Jefferson Jackson Day dinner speech; then to Denver for talks on Western water problems, and he winds it up in Los Angeles at a big fund-raiser to benefit the Democratic National Committee.

Despite his heavy schedule of domestic and international matters, the President will take time out for a social occasion. On Wednesday, daughter Amy observes her 10th birthday and he will be one of the guests at the party.

The next day - one day before he heads West on his political swing - wife Rosalynn leaves on her own campaign trip north to New Jersey to help out in the reelection campaign of Gov. Brendan Byrne. Then on Saturday, the First Lady will visit areas of Virginia to assist Henry Howell in his campaign for state governor Capitol Hill

The House and Senate today begin what most law-makers hope - but many doubt - will be the final two weeks of the current session. Only three pieces of major legislation remain - Carter's energy program, the Social Security financing bill and a supplemental appropriations measure. Any of the three could be a bottleneck in the way of hoped-for Oct. 29 sine die adjournment.

Two of the three bills are slated for House action this week - the supplemental money bill on Wednesday, and the Social Security measure on Thursday. The Senate Finance Committee, still preparing a report on its energy tax bill approved last Friday. The Senate Finance Committee, still preparing a resume on the Social Security bill.

The Senate, which is more or less marking time while the energy tax measure is made ready, has four bills on its calendar this week. They are a tariff bill which, oddly enough, has child care and social services provisions in it; a bill to extend certain GI benefits, and an age discrimination measure. A final vote is slated Tuesday afternoon on the legal services bill. Getting to the energy tax bill possibly by Friday is considered a long shot.

The House program also includes action today on eight bills under suspension of the rules. Among these is the saccharin ban moratorium. Six more suspensions are scheduled for Tuesday, including endangered species and Indochina refugees. Other measures are the energy transportation security bill and exempting disaster payments on certain crops.

One more hand up in the way of adjournment is a compromise on the Labor-HEW appropriations bill. Abortion money has had the bill snarled for weeks and the battling conferees are still undecided on a new meeting for this week.

Heading up committee sessions this week will be the House ethics committee which is finally to open hearings on the Korean scandals. At other committee meetings, the lawmakers will run the gamut from cigarettee racketeering to the high cost of treating kidney disease. Other hearings will deal with postal problems, lumber prices and the risks of operating a gasoline station.

Cigarette racketeering and kidney disease will be the subjects of Senate hearings Friday; cigarettes by a judiciary subcommittee and kidney disease by the finance committee. The House Post Office and Civil Service Committee is meeting Tuesday on what many members consider objectionable reforms in postal service. The Senate Banking Committee will take a look at rising lumber prices Wednesday, while the gasoline station bill will be considered today - along with a deep seabed mining measure - by the Senate Energy Committee.

Committees on both sides of the Capitol will hold hearings on Israel-occupied territories, a judiciary subcommittee in the Senate and an international relations subcommittee in the House. The House International Relations Committee will continue with its Panama Canal treaties hearings Thursday, with Vance and treaty negotiators Ellsworth Bunker and Sol Linowitz as witnesses. U.N. Ambassador Andrew Young will testify today before a House international relations subcommittee on international debt problems.

The Senate Banking Committee will mark up truth-in-lending legislation while the companion House committee is marking up the Safe Banking Act, both on Tuesday. The Senate Commerce Committee on Tuesday opens two days of hearings on a bill to reorganize amateur sports.