A federal jury convicted three New Orleans policemen yesterday of violating the rights of a black man who claimed he was brutally interrogated during a hunt for the killer of a white officer. Four other policemen were acquitted.

The all-white jury convicted Sgt. John E. McKenzie, 40, and officers Dale Bonura, 34, and Stephen Farrar, 31, of conspiracy, a felony, and one count of beating a black witness undergoing interrogation, a misdemeanor. They face a maximum of 11 years in prison and $11,000 in fines at their May 19 sentencing.

Five residents--three blacks and two whites--of New Orleans' Algiers section claimed they were brutally interrogated by officers investigating the Nov. 8, 1980, shooting of Officer Gregory Neupert.

Four blacks were killed by police during the manhunt for Neupert's killer, but no charges were filed in connection with the deaths. The controversy triggered the resignations of the police superintendent and his top lieutenant and prompted a federal judge to move the officers' trial to Dallas.

During deliberations, jurors had asked but were not allowed to re-read the testimony of Oris Buckner, a black officer who admitted he took part in the beating of Robert Davis, a black.

The misdemeanor count on which McKenzie, Bonura, Farrar were convicted alleged that they helped one another assault Davis, depriving him of his civil rights and his right to be kept free from harm while in custody.

The felony count alleged they conspired to threaten and intimidate the residents of Algiers and unlawfully sought information on Neupert's killing by "assaulting, intimidating and threatening" those held for questioning.

Prosecutors contended that the officers were carrying out a vendetta--that they were "willing to take any information they could at any cost."