The Office of Management and Budget has proposed deep cuts in federal education programs next fiscal year, including one that would cut in half the largest of them, the Title I program that now aids 5 million children from disadvantaged homes.

Sources said OMB has also proposed cutting the basic aid program for low-income college students by more than half, cutting vocational and adult education grants by a third and phasing out entirely by 1985 the Department of Education's research arm, the National Institute of Education.

There would also be reductions in politically sensitive programs involving refugee, Indian and bilingual education, according to these sources.

The proposed budget cuts, which Education Secretary Terrel H. Bell is expected to appeal to a White House screening committee and ultimately the president, are among a series OMB is now proposing for all federal agencies in an effort to hold down the projected 1983 deficit. Many of these proposals have been leaked to the press in recent days, in part in an effort to arouse opposition to them.

Some students of the budget process think the administration is deliberately proposing large cuts in these popular aid programs so that Congress will be grateful when it ultimately settles for less, and so that Congress may be tempted also to look for cuts in the big basic benefit or entitlement programs that so far it has left pretty much alone.

"The administration strategy is to show Congress, 'Listen, unless you rein in entitlements, you won't have any discretionary programs,' " one official said. In addition, if Congress fails to make all the cuts President Reagan is proposing next election year and the economy fails to recover, Reagan would be able to blame the legislators.

Reagan also proposed large cuts in education programs in his fiscal 1982 budget but Congress refused to approve most of them. Reagan wants to abolish the Department of Education. The department spent $15.5 billion in fiscal 1981, which just ended. OMB would have it spending under $9 billion by fiscal 1984.

The Title I program, legacy of President Johnson's Great Society, would be cut from about $3 billion a year to $1.5 billion under the OMB proposal.

College aid programs would be cut severely. So-called Pell grants, which now go to 2.5 million mainly lower-income college students, would be cut from $2.6 billion to $1 billion.

The department proposed merging three campus-based programs now funded at $1 billion. But OMB denied the request and has proposed eliminating entirely supplemental grants for the needy and direct student loans. Only campus work-study programs would remain, but funding would drop from $550 million to $400 million.

Vocational and adult education programs currently funded for just under $800 million a year would be slashed to $500 million. The department's Office for Civil Rights would also be cut by OMB, from $47 million to $30 million.

The $500 million block grant Congress approved this year for several federal education programs would be cut by 40 percent, which would give ammunition to opponents who claimed block grants were just the first step to total elimination of federal support for the programs.

Budget director David A. Stockman's proposals also provide only half the $86 million supplemental budget request the department needs to cover the October pay raise for its 5,500 full-time employes.

Under Stockman's current 1983 plan, bilingual programs would be cut in half to about $74 million. The $80 million program for Indian children, who historically have the lowest test scores of any minority group, would be slashed to $43 million. Funding for an $11 million program to help refugees, mostly Cubans and Haitians in south Florida learning English, would be eliminated.

The only program to escape unscathed is the $130 million Title III program for "developing institutions," which was designed to aid traditionally black colleges. The president promised black college presidents earlier this year that he would encourage government programs to assist them.