A Senate committee yesterday approved eight of President Reagan's nominees for the beleaguered Legal Services Corp. One nominee squeaked through by one vote, and the vote on another, who faced a tougher fight, was deferred at the last-minute request of the White House.

The Reagan administration wants to abolish the corporation, which provides legal help to the poor, and agency supporters have criticized the nominees, saying they are not familiar with the agency or committed to its work.

But the Labor and Human Resources Committee approved the eight nominees it considered, and Chairman Orrin G. Hatch (R-Utah) said he expected the full Senate to confirm them before the August recess.

Two nominees received some "no" votes. William J. Olson, a lawyer here, was approved on an 8-to-7 vote, and three senators voted to reject the nomination of William F. Harvey, an Indiana University law professor.

Hatch said the White House called his office shortly before the hearing and asked that the committee defer a vote on the nomination of Sacramento attorney George E. Paras. Hatch said he did not know if Paras' name would be withdrawn. A White House spokesman said the status of Paras' nomination was unchanged, and declined further comment.

Paras' secretary said he was unavailable because of the death of his son.

At hearings in May, Paras' nomination drew fire because of a letter he had written to Cruz Reynoso, the first Hispanic judge nominated to the California Supreme Court. The letter said, "Your problem is that you feel it your obligation to be a professional Mexican rather than a lawyer."

Paras later attempted to clarify that statement: "There are such things as professional blacks, professional Greeks, professional Dagos, professional Jews, people who put their ethnic origin ahead of everything else. That's what I meant."

In addition to Harvey and Olson, the committee cleared the nominations of Howard H. Dana Jr. of Portland, Maine, Harold R. DeMoss Jr. of Houston, William L. Earl of Miami, Clarence V. McKee of the District, Annie L. Slaughter of St. Louis and Robert S. Stubbs II of Atlanta.