Because of budget cuts, all three major federal civil rights agencies will be scaling back the level of services for people seeking protection from discrimination.

The staff of the Equal Employment Opportunity Commission (EEOC), set up 15 years ago to enforce civil rights laws in employment, will be reduced by nearly 10 percent under a cut of about $20 million next year, according to testimony before a House Appropriations subcommittee yesterday. A $32 million cut is slated for the year after.

A years-old backlog of discrimination cases scheduled to be eliminated by 1982 now must be carried until the end of 1983, according to EEOC acting chairman J. Clay Smith, and the processing of new cases will be slowed. The investigation of complaints by federal employes will be left to the agencies that employ them, rather than being handled by the EEOC.

All programs will be "modified" but it is too early to tell how, he told the subcommittee.

The smaller Office for Civil Rights, in the Department of Health and Human Services, will lose 10 percent of its staff, dropping to 524 positions, with a cut of nearly $900,000. The agency enforces several civil rights laws in schools, colleges and other institutions that receive federal funds.

"We will scale down to some extent our compliance review activity and technical assistance services," said agency spokesman Bill Vandentoorn.

The Labor Department's Office of Federal Contract Compliance (OFCCP), which enforces antidiscrimination laws in organizations working under federal contract, will lose roughly 6 percent of its employes over a two-year period.

As a result of the cuts, the number of reviews it expects to perform to determine whether contractors are complying with the law will be reduced by about 20 percent the first year, to 3,092. Instead of increasing to 4,250 the second year, as previously scheduled, the agency will hold at 3,092, Charles E. Pugh, a Labor Department official, said.

OFCCP also will reduce the level of follow-up actions, such as court orders against violators, from 8,353 next year to 6,682.

The agency has had a high worker turnover rate, he said, and there are a substantial number of new employes being trained. The decline in enforcement activity would be even greater, he said, except that "we expect that training to show up [by 1982] in increased productivity, enough to offset the decrease in the number of employees."

The budget cutting has thrown a wrench into the antidiscrimination machinery at these three agencies when it was just beginning, slowly but visibly, to have some effect.

After years of confusion and poor management at EEOC, for example, Eleanor Holmes Norton, the departing chairman, had reported the first permanent reduction in an enormous case backlog, from 99,000 in 1977 to 56,000 in 1979 and still declining.

Rep. Joseph Daniel Early (D-Mass.) urged yesterday that the agency make its cutbacks in such a way that cases not be allowed to drag on past six months. "I thought Ms. Norton made a good case that one of the worst problems was letting them go on too long," he said.

EEOC's problems are compounded by the fact that its workload keeps increasing, Smith noted.

It was recently given jurisdiction over age discrimination, complaints under the equal-pay-for-equal-work law, and federal, in addition to private, employment discrimination cases. These compete for the agency's resources with the 80,000-a-year so-called Title VII cases involving race, sex, religion, national origin and handicapped workers.

The fastest-growing category is age discrimination, which is bringing in some 8,000 new cases a year, Smith said.