The Supreme Court, entering a gay rights controversy for the first time in years, agreed yesterday to consider whether an Oklahoma law barring schoolteachers from publicly advocating homosexuality violates the right to free speech.

The case was among 31 the court accepted for review yesterday on the first day of its 1984 term. The court also agreed to consider controversies over state obscenity laws, the power of the Securities and Exchange Commission to ban publication of investment newsletters, restrictions on lawyer advertising and the denial of a driver's license to a Nebraska woman who refused on religious grounds to have her photograph taken.

As a result of yesterday's actions, the 1984 term features an unusual concentration of six major First Amendment free-speech cases and four major religion cases. The court is being watched especially closely in these areas because of a perceived "rightward" tilt, led by an increasingly solid conservative majority.

In other action yesterday, the court declined to review a Rhode Island Supreme Court decision earlier this year throwing out the conviction of Claus von Bulow for the attempted murder of his wife. Rhode Island may now retry von Bulow but without the critical evidence excluded by the state supreme court.

Board of Education v. The National Gay Task Force stems from a challenge by a national gay rights group to Oklahoma's law allowing the dismissal of teachers who engage in "public homosexual conduct. . . in a manner that creates a substantial risk" that it will come to the attention of schoolchildren or employes. Its definition of conduct includes "advocating . . . encouraging or promoting public or private homosexual activity."

A divided three-judge federal appeals court panel agreed that the law impermissibly infringed on teachers' rights to free speech.

The Oklahoma City Board of Education says the free-speech rights of teachers "are not absolute and may be subjected to certain restrictions" in order to rid the school system of teachers who are "unfit."

In the SEC case, the court will consider whether the First Amendment permits the agency to ban publication of newsletters dispensing investment advice.

The case, Lowe et al. v. SEC, involves a provision of the Investment Advisers Act, which allows the government to revoke the registration of investment advisers in order to protect the investing public. In 1981, the SEC moved to bar publication of three investment newsletters published by Christopher L. Lowe, on the grounds that his registration as an adviser had been previously revoked for investment-related criminal violations.

Such a ban, if enforced against an ordinary newspaper, would be considered an unconstitutional form of "prior restraint" of the press. The 2nd U.S. Circuit Court of Appeals upheld the government's action, however, saying that it fell within its authority to regulate business activity and that it was a valid restriction on "commercial speech."

The Financial Publishers of America, a trade association of hundreds of publishers of financial information, urged the court to review the lower court decision, saying it would permit "total censorship" by the SEC.

The lawyer advertising case, Zauderer v. Office of Disciplinary Counsel, involves an ad for legal services for women picturing a Dalkon shield intrauterine device, which has been the subject of years of litigation because of side effects that injured its users. "Did You Use This IUD?" said the ad for Philip Q. Zauderer & Associates of Columbus, Ohio. It brought a reprimand from the Ohio Supreme Court for using a picture of the device in violation of Ohio Supreme Court rules.

Zauderer, citing recent Supreme Court decisions limiting restrictions on lawyer advertising, is arguing that the reprimand violates his free-speech rights.

The obscenity cases from Washington, Brockett v. Spokane Arcades and Eikenberry v. J-R Distributors, et al., centers on the word "lust." The state passed a new obscenity statute in 1982 that said, among other things, that speech that excited "lust" could be banned. A federal appeals court ruled that the term "lust" was too broad and could ban anything a jury thought would stimulate sexual desire.

State officials charged that the appeals court misinterpreted Supreme Court precedent on obscenity and overstepped its authority, interfering with state courts and legislatures.

The driver's license case, Jensen v. Quaring, began when Frances J. Quaring refused to have her photograph taken for inclusion on a Nebraska driver's license, citing the Second Commandment: "Thou shalt not make unto thee any graven image . . . . "

Quaring unsuccessfully sought a license without a photograph, arguing that having her picture taken for the license would violate her right to the free exercise of religion. The 8th U.S. Circuit Court of appeals ruled that the state should accommodate her by granting the non-photographic license. Nebraska appealed to the Supreme Court.

In other actions yesterday, the court:

*Agreed to review the scope of a city's liability for damages for civil rights violations by its police officers. The case, Oklahoma v. Tuttle, stems from a $1.5 million damages award won by the family of a suspect shot in the back and killed by an Oklahoma City police officer. The city contends that while it may be held responsible for misconduct stemming from an official policy or practice, it cannot be accountable under civil rights laws for an "isolated incident."

*Said it would consider the standards employers must meet to disprove charges of age discrimination under federal law. The case, Western Air Lines, Inc., v. Criswell, involves a suit by pilots challenging an age-60 mandatory retirement policy.

*Agreed to consider whether airlines may be held liable for passenger injuries that are not caused by the malfunction of an aircraft or by an accident. Air France brought the appeal (Air France v. Saks) after it was held liable for a total and permanent hearing loss suffered by Valerie H. Saks as a flight was landing in Los Angeles. Air France contends that the Warsaw Convention, limiting international air carrier liability, bars such liability. The 9th U.S. Circuit Court of Appeals said that another air travel agreement, the Montreal Agreement, imposes "absolute liability on airlines for injuries caused by air travel."

*Agreed to decide whether unions can discipline members who quit the union during a strike or lockout and return to work. The case, Pattern Makers' League of North America v. National Labor Relations Board, involves a group of members who did so in 1977.

*Agreed to consider how much protection from dismissal union contracts give government employes. The case, Devine v. Nutt, involves two federal building guards in Denver fired over a beer-drinking incident.

*Denied review in two civil rights cases, including a challenge by Birmingham, Mich., to a housing discrimination suit against it (Birmingham v. U.S.) and a lower court ruling upholding a minority "set-aside" provision for contracts let by Dade County, Fla.

*Left intact two-year-old federal regulations requiring the nation's funeral homes to provide detailed information to customers. Seven funeral homes, representing the entire industry, challenged the rules, which were designed to provide consumers with more information about funeral prices and prevent deceptive practices (Harry & Bryant Co. v. FTC).

*The court refused to get involved in controversies over the liability of drug companies for damages to women caused by the pregnancy drug DES (Squibb & Sons v. Collins et al.); over the constitutionality of federal laws against corporate participation in anti-Israel Arab boycotts (The Trane Company v. Baldridge); over zoning ordinances that prohibit residential homes for the mentally retarded in some neighborhoods (Macon Association for Retarded Citizens v. Macon-Bibb County Planning and Zoning Commission) and over a Massachusetts law banning charitable solicitations over the telephone (Bellotti v. Planned Parenthood of Massachusetts).