The Supreme Court, opening its 1981 term yesterday, agreed to review major controversies involving voting rights, bail, defamation in television broadcasts, and, most significantly for the federal government, the power of a single house of Congress to veto executive branch decisions.

The "legislative veto" case is considered one of the most crucial balance-of-power contests in years between the executive branch and Congress. Numerous laws allowing a single house to veto regulatory and immigration actions are at stake, and a broad opinion from the court conceivably could affect, for example, Congress' authority to block the sale of AWACS planes.

The case accepted yesterday involves an immigration law provision under which one house can expel a foreigner from the United States even though the attorney general has allowed him to stay. Jagdish Rai Chadha, from Kenya, was to be deported for overstaying his visa when he appealed successfully to the attorney general for permission to stay as a "hardship" case. If he were sent back, he said, his Indian ancestry would subject him to discrimination in Kenya.

The law allows either house to veto such a decision by the attorney general, but such a veto occurs rarely. This time, however, Rep. Joshua Eilberg (D-Pa.), objected to five decisions, including the one involving Chadha, and the House vetoed them.

The Court of Appeals for the 9th Circuit last year sided with Chadha and the attorney general, striking down the immigration law provision. Both houses have to concur in the enactment of laws, it said.

The government has called the controversy a constitutional issue "of the most fundamental nature regarding the distribution of powers among the branches of the federal government." The legislative veto would allow a "dangerous" concentration of power in one branch, the executive branch argues. Congress could enact laws permitting one of its houses to disapprove any action by the president or the executive branch, the solicitor general says.

Congress has hired its own lawyer for the case, Supreme Court expert Eugene Gressman, and is arguing that the legislative veto is an example of "government coordination," not usurpation of authority. To eliminate the veto would confer "unlimited power" on the executive branch, Congress argues.

A Supreme Court opinion, expected by July, could be confined to the circumstances of this case. But if the court fully accepts the executive branch's argument--that there is only one way for Congress to act, with both houses and a presidential signature as set out in the Constitution--it could have a broader impact. It could, for example, figure in any unusual use of congressional power, such as the ability of two houses to veto the sale of AWACS planes, or, some lawyers speculate, the current power of one house to override actions of the D.C. government.

In other action yesterday:

The justices announced consideration of a crucial voting rights case in which an at-large system for electing county commissioners was ruled discriminatory and ordered changed by a federal court.

The case (Rogers vs. Lodge) stemmed from a challenge by blacks to the at-large system of electing the commissioners of Burke County, Ga. Blacks constitute 60 per cent of the 18,000 residents of the county, but they have never held elective office. They charged there, as they have throughout the south, that at-large systems, as opposed to district or ward election systems, tend to dilute the black vote.

The 5th U.S. Circuit appeals court ordered the county to switch to a district system, saying that the "inference of discriminatory intent" was clear in the design and impact of the county's at-large system.

County officials are arguing that an "inference" is insufficient grounds for such a court order. The blacks, they say, must prove specifically that the at-large system was set up with the aim of excluding blacks.

The issue--the need to prove intentional discrimination and the standard for proving it--is the same one addressed last year by the court in a similar case from Mobile, Ala. That ruling resulted in confusion, however, because only four justices signed the opinion.

Civil rights lawyers contend that rigorous requirements for a showing of intent will doom efforts throughout the South to eliminate allegedly discriminatory voting systems.

The court said it will review a Nebraska law that automatically denies bail to certain defendants facing a serious rape charge. Generally, judges have discretion to set bail or to deny it in murder cases to ensure that a defendant shows up for trial. But in 1976, a statewide referendum in Nebraska produced a state constitutional amendment denying bail to alleged rapists or murderers against whom there is strong evidence, regardless of other factors.

Eugene L. Hunt challenged the law after being denied bail on a sexual assault charge. A federal appeals court threw out the Nebraska law, ruling in Roth vs. Hunt that a denial of bail, without consideration of individual circumstances, violated a constitutional prohibition on excessive bail. The lower court said that prohibition applied to the states.

The court announced review of a case brought against NBC-TV by the chief witness in the famous Scottsboro Boys trials in the 1930s. Nine blacks were accused of raping two white women on a freight train traveling from Tennessee to Alabama. The death sentences of the blacks, who had been denied legal counsel, created a storm of international publicity before the sentences were reversed by the Supreme Court.

NBC aired a television film in 1976 and again in 1977 dramatizing the Scottsboro case. At the center of the drama was Victoria Price Street, a major accuser of the blacks. Street later sued NBC, charging that the network portrayed her as a "whore" and "perjurer."

The 6th U.S. Circuit Court of appeals threw out her defamation suit, however, ruling that she is a "public figure" who must prove that the network acted with "malice" in its portrayal.

The public figure question is crucial to all libel and defamation cases. A public figure must show that he or she has been libeled or defamed because of actual malice. Winning such a case generally becomes impossible. A Supreme Court opinion narrowing the definition of public figure would significantly aid people suing media organizations.

The court entered the controversy over "parental rights," accepting an appeal from a woman whose children were permanently taken away by the courts in New York. The woman, in a procedure standard throughout the country, lost her family after social workers alleged that she couldn't properly care for them.

Federal courts rebuffed Marjorie Lehman's efforts to win back her children, saying that such cases were state matters, without the fundamental constitutional liberty issues required for federal intervention. The justices will consider that contention in Lehman vs. Lycoming County Children's Service Agency.

The justices agreed to decide whether the University of Maryland must allow all aliens living in the state to take advantage of "in-state" tuition and fee benefits. Currently, the benefits are available only to U.S. citizens and foreigners who intend to establish permanent residence in the United States.

Yesterday's case, Toll vs. Juan Carlos Moreno, was brought on behalf of children of World Bank and International Development Bank employes, who successfully appealed the Maryland rule to the 4th U.S. Circuit Court of Appeals.

Maryland argued that the exclusion of nonimmigrant aliens was justified primarily by the fact that they do not make the same contribution through taxes to the cost of education in the state as citizens or permanent residents.

The court accepted a case (Connecticut vs. Winnie Teal) involving allegedly discriminatory tests for promotion given to employes of the state of Connecticut. Black employes charged that the test was plainly discriminatory because it precluded a disproportionate number of blacks from moving up.

The justices agreed to consider U.S. bilateral agreements which give preference in jobs on military bases to host country citizens. The case, Wineberger vs. Rossi, stems from a successful challenge to the preference brought by Americans seeking work at the Subic Bay naval base in the Philippines.

The court announced 23 cases for review yesterday and rejected hundreds. Those rejected included a suit brought by the family of Karen Silkwood, an employe of an Oklahoma nuclear fuel plant who was killed in a hit-and-run accident in 1974 while on her way to a meeting with a New York Times reporter. The family sued Kerr-McGee Corp., which operated the plutonium facility and the FBI, charging harassment and intimidation under civil rights laws. The lower courts dismissed the suit.

The court also declined to enter the debate currently raging over whether adoptees have a right to find out the names of their natural parents.

It rejected the appeal of South African prize fighter Nikolaas (Kallie) Knoetze to be permitted to fight in the United States. The government revoked his visa last year because of his involvement as a South African police officer in the shooting of a black youth.

The court refused to allow Morton Halperin, former White House national security adviser, to participate in a damages suit brought by former Pentagon whistleblower Ernest Fitzgerald. Both men seek money damages from former president Nixon and Nixon aides. Halperin, whose case produced a tie vote last year in the court, said the Fitzgerald case would affect him as well.