A Nevada man who has fought deportation for the past 11 years was granted a new trial yesterday by the Supreme Court.

In a 7-to-2 decision, the court majority ruled there was a question as to whether Joseph V. Agosto was born in the United States, as he claims, or in Italy, as the government asserts.

The issue should be decided in federal district court, even though an immigration judge and an appeals board for the Immigration and Naturalization Service did not believe Agosto's story, the Supreme Court said.

In a sharply worded dissent, Justice Lewis F. Powell Jr. said the majority ruling, "rewards falsehood and frustrates justice."

Noting that Agosto has a record of criminal convictions and had changed his story about his personal background more than once, Powell said: "There can be no case less deserving of further factual review than this one."

By granting Agosto a new trial, Powell said he will be "free to change his testimony - again - and to round up new witnesses who will swear to it." Justice William H. Rehnquist joined in the dissent.

Justice Thurgood Marshall, in the majority opinion that overturned a ruling by the 9th U.S. Circuit Court of Appeals, said the lower court was "not at liberty to deny an individual" a new trial in a deportation case because it did not believe him and his witnesses. A question of facts should be determined at the trial level, he said.

Agosto, described by his lawyer as a Las Vegas businessman with numerous holdings in that city, claims he was born in Cleveland. The government says he was born in Agrigento, Italy, in 1927.

Agosto claimed that while an infant, his mother, who lived in Cleveland, sent him to live with her sister's family in Italy. Agosto said he later took the name of that family, Pianetti.

Members of the Pianetti family testified to that history in immigration hearings but the immigration judge did not believe them.

In other actions: WELFARE

The court ruled unanimously that states are entitled to set their own standards for deciding who should get emergency welfare aid under a federally subsidized program.

The ruling overturned a decision by the 7th U.S. Circuit Court of Appeals that struck down an Illinois welfare funding plan.

That program was aimed at giving emergency assistance to welfare families who are homeless because of a disaster or through eviction. It excluded emergency aid to other needy families who would generally qualify for welfare.

Justice Potter Stewart said in the court's 8-to-0 opinion that even though the program relied upon federal funds, there was nothing in the law to prevent states like Illinois from adopting their own eligibility standards.

Illinois' emergency aid program was challenged in 1974 by a group of welfare recipients who said their equal protection rights were violated.

Justice Harry A. Blackmun did not take part in considering the case. NAZI RALLY

The villagfe of Skokie, Ill., where many Jewish survivors of the World War II Holocaust live, asked the Supreme Court to rule that it can ban Nazi demonstrations without running a foul of the Constitution.

Village officials urged the justices to overturn a 7th U.S. Circuit Court of Appeals ruling voiding three ordinances designed to prevent a planned June 25 demonstration by the National Socialist Party of America in the Chicago suburb.