Vernon E. Jordan Jr., one of the country's most prominent and outspoken civil rights leaders, is expected to resign as president of the National Urban League today to join the law firm of former Democratic National Chairman Robert S. Strauss.

A source at the Dallas-based firm of Akin, Gump, Strauss, Hauer & Feld, which maintains a Washington office of about 100 lawyers, said the announcement will be made at a news conference at the Urban League in New York.

Jordan's expected resignation comes at a time when the league, a 71-year-old organization with 118 affiliates around the country, faces severe financial pressures resulting from President Reagan's budget cuts.

This summer at the league's annual convention, Jordan leveled a broadside against Reagan's "jellybean budget," and noted that "even the wildest optimist knows it will take years for the president's program to produce the prosperity he promises. What do we do until then?"

League aide Vernice Williams said the budget cuts will hit hard at two of the league's most important programs: one that trains minorities and women for jobs in the construction trades, and another that provides technical assistance to community groups on how to apply for and administer Comprehensive Education and Training Administration (CETA) job programs. She said the league could lose up to 80 percent of its funding for those programs.

A towering figure of a man with movie star looks, Jordan, 46, is known for his smooth, lawyerly style, his ability to attract major corporations to the cause of civil rights and, perhaps most of all, for the bullet that nearly took his life.

Sixteen months ago he was shot in the back as he emerged from his car in the parking lot of a motel in Fort Wayne, Ind. The rifle shot left a wound the size of a fist an inch from his spine. Jordan underwent five operations before leaving the hospital 98 days later.

Although the attack, for which no one has yet been charged, made a martyr of Jordan, it also led to a whispering campaign against him because he was accompanied by a white woman at the time he was shot.

Some believe this may have damaged Jordan's standing in the civil rights movement, especially among black women, although there is no evidence that this played any part in his expected resignation.

Jordan, who has been married for 23 years, has said of the gossip, "I view that as their problem, not mine. I have to define the parameters of my life and my morality. I have to be accountable. The focus, it seems to me, should be on the shooting itself, instead of what else might have been going on."

A source in the legal community said it was Strauss who broached the idea to Jordan about joining the law firm, rather than the other way around. Strauss, who was chairman of Jimmy Carter's reelection campaign, has been mentioned as a possible presidential contender in 1984, and the wooing of Jordan could be construed as a effort to shore up his ties to the black community.

Jordan, who spent part of his youth in the public housing projects of Atlanta, began his civil rights career as Georgia field director for the NAACP. He served as director of the United Negro College Fund before taking over the league as president in 1972.

His resume is studded with corporate and foundation directorships, including the Bankers Trust Co., Celanese Corp., MIT Corp., J.C. Penney Co., Xerox Corp., the John Hay Whitney Foundation and the Rockefeller Foundation.