Fifty-seven congressmen sent a letter to Paraguayan President Alfredo Stroessner yesterday urging him to extradite Dr. Josef Mengele, a Nazi accused of supervising the murder of more than 400,000 people at Auschwitz during World War II.

Three of the congressmen held a press conference to say that a trusted source in Paraguay knows the whereabouts of Mengele, but will reveal them only on condition that he be extradited to Israel or West Germany. Their announcement coincides with recently submitted resolutions in the House and Senate asking President Carter to call for Mengele's extradition.

The 68-year-old Mengele has been called the "angel of death of Auschwitz" because he determined which prisoners would be sent to the gas chambers. He is also reputed to have performed experiments using camp inmates as guinea pigs.

Congressmen Matthew F. McHugh (D.-N.Y.), Christopher J. Dood (D-Conn.) and Robrt K. Dornan Jr. (R.-Calif.) claimed they have proof that Mengele was made a Paraguayan citizen in 1959, but the Nazi's whereabouts have been in dispute for more than 20 years.

During that time, he is reported to have been spotted throughout Latin America, in Canada and Europe. West Germany has twice requested his extradition from Paraguay, but Stroessner has denied knowledge of Mengele's whereabouts.

Congress is considering giving almost $4 million in economic aid to Paraguay in 1980. Asked if that might be used as leverage. McHugh, who is on both the House Appropriations Committee and foreign operations subcommittee, said, "There are questions we'd prefer to defer until the government makes a response to our initial contact." CAPTION: Picture, PRESIDENT STROESSNER . . . previously denied hiding Nazi