The Supreme Court yesterday agreed to consider whether the nation's oldest all-female public university must admit men.

The justices will review a lower court determination that the Mississippi University for Women, established in 1884, unconstitutionally discriminated against men by denying Joe Hogan admission to its nursing education program.

A clear Supreme Court ruling on the issue would settle a controversy that has produced conflicting opinions from lower courts in different parts of the country.

In the Mississippi case, the state argued that nursing education programs open to men at other state schools afforded Hogan the opportunity he sought. The 5th U.S. Circuit Court of Appeals ruled, however, that the lack of any comparable all-male university in Mississippi demonstrated that men and women were being treated unequally by the state in violation of the U.S. Constitution.

The alumnae association of the women's school joined the state in seeking Supreme Court review. While a state university could not legitimately exclude women, it said, the exclusion of men was justified by the need to overcome past discrimination against women.

The justices also agreed yesterday to review another discrimination question: whether American law prevents a Japanese-owned company operating in this country from discriminating against American women.

A group of women sued Sumitomo Shoji America Inc., challenging its policy of filling management positions exclusively with Japanese men. The women, secretaries at the firm's New York office, said the policy violated Title VII of the U.S. Civil Rights Act of 1964. The company said the law did not apply to it because of a U.S.-Japan treaty allowing it to make its own hiring decisions.

The 2nd U.S. Circuit Court of Appeals ruled that federal civil rights law did cover the firm. But it also allowed an interpretation of the law generous to the foreign firm, saying that special needs, such as language and cultural requirements for employment, might permit some otherwise impermissible discrimination against Americans. The justices will consider both issues.

In other action yesterday:

* The court agreed to review an important issue of libel law in a case involving WMC-TV in Memphis and a 1975 story alleging that a Mississippi cattle owner was starving his cows. The owner, Shelby T. Wilson, sued, alleging that the story was false, and won a $30,000 judgment. In the trial, the U.S. District Court told the jurors that the television station had the obligation to prove its story was true. That prompted a reversal by an appeals court, which said the person suing has to prove the falseness of the story to prevail in a libel case.

The question of who has the burden of proof is crucial in the law and can tilt a case decisively. A Supreme Court ruling that the media organization must prove the truth of its reporting could significantly ease the task of libel plaintiffs. But a ruling in the Tennessee case, in which Wilson was considered a private person, would not affect suits brought by prominent public figures, who must prove malice on the part of the news organization.

* In another libel case, the court allowed C. G. (Bebe) Rebozo's $10 million suit against The Washington Post to go to trial over the objections of the newspaper. Rebozo, a close friend of former president Nixon, sued the paper over a Watergate-era story that reported there were allegations that he had cashed thousands of dollars worth of stocks after being told they were stolen.

A U.S. District Court in Florida originally dismissed the 1973 suit, saying there was nothing for a jury to consider in the case. The 5th U.S. Circuit Court of Appeals, however, said a jury should consider whether reporter Ronald Kessler acted with "malice" in his reporting of the story. The justices also declined yesterday to hear Rebozo's contention that he was not a public figure and thus should not have to show malice on Kessler's part.

* The court said it will consider how much special help public schools must provide deaf students. The Hendrick Hudson Central School District in Westchester County, N.Y., asked for Supreme Court review after it was ordered to provide a sign language interpreter for Amy Rowley, a deaf elementary school student.

The school was already providing a hearing aid, therapy and special tutoring, but the lower courts said that was not enough under the Education for All Handicapped Act. That law, which applies to all schools receiving federal aid, has been the focus of continuing challenges from school systems around the country which contend that it imposes excessive spending requirements on them.

* The court said it will review a major labor controversy stemming from the 1977 challenge by insurgents to the leadership of the United Steelworkers of America. Edward Sadlowski Jr., the unsuccessful candidate for Steelworkers president that year, campaigned with the help of significant outside support, including legal assistance from outside the union. Afterward, the union convention banned contributions in any form from nonmembers. The rule was challenged by Sadlowski and his allies, and was struck down by the Court of Appeals for the District of Columbia as a violation of free speech guarantees of federal labor law.

* The justices will consider in Middlesex Co. Ethics Comm. vs. Garden State Bar Assn. whether federal courts can intervene in lawyer disciplinary proceedings. The court agreed to review a New Jersey federal court intervention in a bar proceeding against Lennox Hinds, then president of the National Conference of Black Lawyers, who was accused of breaching lawyer ethics by publicly attacking the judge in the trial of a woman for the murder of a New Jersey state trooper. Hinds sued in federal court, saying the ethics code in question violated the First Amendment's free speech protections. Bar disciplinary actions are generally exclusively state proceedings.

The court will consider whether federal unemployment tax laws apply to church-related schools. It agreed to hear arguments in three cases (California vs. Grace Brethren Church, etc.,.) from California.

* The court let stand an important auto pollution ruling that upheld Environmental Protection Agency regulations on emission levels for diesel engines. The EPA rules require manufacturers to slash diesel engine pollution by as much as 25 percent on some vehicles by 1985. The ruling, from the Court of Appeals for the District of Columbia, was challenged by General Motors Corp., Mercedes-Benz and Volkswagen.