The Office of Management and Budget is proposing deep new spending cuts in two of the government's most popular urban aid programs and in the program that helps pay the heating bills of the poor, sources said yesterday.

OMB wants to allow only $156 million for urban development action grants (UDAG) in fiscal 1984, a two-thirds reduction from the $440 million in this year's budget, sources said.

Mayors use the action grants to attract private investment for hotels, convention centers, industrial parks and other projects.

Budget officials also want to cut community development block grants, to which nearly all cities are entitled, by $330 million to $3.12 billion in fiscal 1984.

Housing and Urban Development Secretary Samuel R. Pierce Jr. is preparing to appeal both reductions to the White House, as he did successfully last year when OMB tried to phase out the urban aid programs, sources said.

In fuel assistance for the poor, a program that is highly popular on Capitol Hill, OMB is proposing $1.3 billion for fiscal 1984, a one-third cut from Congress' tentative figure for fiscal 1983.

According to the latest figures available, the program helps pay fuel bills for about 18 million people each year, or 7 million households.

OMB, at President Reagan's behest, is trying to make $25 billion to $30 billion in domestic spending cuts next fiscal year to hold down the likely 1984 deficit while protecting the president's proposed defense buildup. But such cuts are sure to be controversial on Capitol Hill and among the affected interest groups.

Urban leaders, while grateful to Pierce for defending the urban programs, are bitterly disappointed at the proposed cutbacks. Mayors consistently point to the two grant programs, along with revenue sharing, as their most vital sources of federal aid.

"This is just an unconscionable cut," said a spokesman for the U.S. Conference of Mayors. "We were promised that these programs would not be cut again."

"It comes as a real shock," said Alan Beals, executive director of the National League of Cities. "I thought we had convinced the administration that these programs play a very important role in strengthening the economies of the cities and creating jobs."

OMB proposes to reduce the action grants by deferring $234 million in spending already approved by Congress from this year until fiscal 1984, sources said. Similarly, $221 million of this year's $3.45 billion in community development grants would be deferred until fiscal 1984. Fiscal 1984 appropriations would then be reduced accordingly.

Supporters say the action grants have attracted about $6 in private capital for every federal dollar spent on such projects as Washington's Hechinger Plaza, Baltimore's Harborplace and Detroit's Renaissance Center. Most cities use community block grants for housing rehabilitation, sewer construction and street repair.

At the Health and Human Services Department, it was learned, OMB has decided to seek $1.3 billion in fiscal 1984 to help low-income people pay their home fuel bills -- a cut of $550 million from the $1.85 billion that both the Senate Appropriations Committee and the House have just approved for fiscal 1983.

According to documents obtained by The Washington Post, OMB Director David A. Stockman also wants to rewrite the distribution formula to restrict this aid to states with severe winter climates, a concept that HHS Secretary Richard S. Schweiker described as "highly controversial" in a letter to Stockman appealing some of the cutbacks.

In addition to the deep cuts in department personnel and in health programs reported earlier this week, Stockman is proposing these other changes in discretionary programs at HHS:

* $1.015 billion in fiscal 1984 for Head Start, which at first blush looks like a big increase over the $912 million that Congress is voting for this year, but actually is not. About four-fifths of the added money would go to pay for Head Start food costs now paid for by the Agriculture Department, so the basic program increase is only about $20 million.

* Transfer of four programs to HHS from other departments, including the Head Start food program. The others are: a $277 million employment program for older Americans, from the Labor Department; the Work Incentive Program for training and placing welfare clients in jobs, which Stockman proposed to transform into a block grant and to fund at $140 million (a 50 percent cut), and a $100 million food-distribution program that makes use of surplus agricultural commodities.

* Creation of a block grant for refugee aid, but cut 15 percent below Schweiker's $485 million request, and child welfare and children's services block grants, combining several small programs.

* A cut of 437 in Schweiker's request of 1,200 employes for the Office of Human Development Services, which handles many of the programs for children and the aging, and elimination of all the office's research funding.

In other areas, sources said OMB is proposing to cut the staff at the Education Department's Office for Civil Rights from 948 to 861. OMB also wants to eliminate Agriculture Department funding for nationwide food consumption surveys, which are used to determine whether people have adequate diets and to set minimum dietary standards for the food stamp program.