The House Education and Labor Committee, in one of the first congressional rebellions against the Reagan administration's proposed budget cuts, yesterday rejected by party-line votes of 20 to 14 almost every dollar of the $14 billion President Reagan wants to chop from the programs within the committee's jurisdiction.

With Democrats voting as a bloc, the traditionally liberal committee then went further. In a report to the House Budget Committee on its plans for this year, it voted to add $1 billion for impact aid to school districts with large numbers of federal employes and for various job programs that even former president Carter had proposed cutting.

Among programs Reagan wants to cut and the committee voted to preserve are aid to elementary and secondary education, aid to college students, child nutrition subsidies, public service jobs, occupational health and safety and mine safety efforts and many others.

However, cuts Reagan has proposed in other social programs won approval from two House Ways and Means subcommittees, albeit with amendments.

The public assistance subcommittee approved a net saving of $4.1 billion in welfare, social services, child welfare, unemployment insurance and low-income heating assistance, the same figure Reagan has sought.

But it specified from taxing of the total should come from taxing unemployment insurance benefits whenever they help push a taxpayer's income from all sources over $15,000 a year, or $20,000 for a married couple.

By raising $1 billion extra revenues through the tax, which Reagan hadn't proposed, the subcommittee plan would allow some of the other programs to be cut less while still saving the total he wants.

The subcommittee on trade approved Reagan's request for a cut of approximately $1 billion in trade-adjustment assistance (extra unemployment benefits for workers idled by imports), with slight revisions.

Budget battles also continued elsewhere on Capitol Hill:

Robert Greenstein, former administrator of the Agriculture Department's food and nutrition service, told a House Agriculture subcommittee that "the overwhelming bulk of the savings" from Reagan's request for a; $1.8 billion food-stamp cut "comes from persons below the poverty line."

Labor Secretary Raymond J. Donovan told the House Budget Committee that the administration continues to believe in job training, despite cuts. "We are still training-oriented, heading toward private-sector employment," he said.

Attorney F. William McAlpin, chairman of the board of the Legal Services Corp., asked a House subcommittee to extend his agency for three more years, with $400 million for fiscal 1982, $450 million for fiscal 1983 and $500 million the next. He said Reagan's plan to kill the program would be a blow to assuring equal justice to the poor.

Secretary of Health and Human Services Richard S. Schweiker told the Senate Finance Committee that all 658,000 families that would lose benefits under Reagan's proposed welfare rules changes could be classified as above the official poverty line ($8,410 for a family of four) if their food-stamp benefits and the income of step-parents and persons acting as step-parents in the home were counted,.

But some welfare experts disputed Schweiker's figures, saying welfare levels are so low in some southern states that anyone being pushed off or cut in those states couldn't be above the poverty line even counting food stamps and step-parent income.