The Office of Management and Budget has proposed cutting the non-defense portions of the Energy Department budget by more than one-third next fiscal year, virtually eliminating spending for solar and fossil fuels research and conservation, it has been learned.

OMB wants DOE to have only $9.3 billion in new budget authority next year, $5.1 billion less than the department originally asked and $2 billion less than this year's appropriation.

Defense programs and nuclear warheads account for about more than half of the $9.3 billion, while another $2.3 billion would be earmarked for filling the strategic petroleum reserve. Nuclear energy research would take about half of the remaining $2 billion, with about $250 million slated for the controversial Clinch River Fast Breeder Reactor in Tennessee.

In contrast, budget authority for all DOE conservation programs would fall to only $19 million in 1983. Last year such programs got $712 million. Solar research and demonstration programs, which got half a billion dollars in 1981, would end up with only $70 million in 1983.

Research on fossil fuels -- coal, oil and natural gas -- which was a $1 billion effort in 1981, would plummet to only $107 million.

In addition, OMB wants much of the cost of research into finding a permanent solution for storing nuclear wastes shifted to the nation's utilities. The budget agency has given DOE 30 days in which to come up with a legislative proposal to accomplish this goal. Altogether, the cuts apparently would mean a loss of about 4,000 jobs at DOE, which had 19,567 employes at the end of September, and which the president has pledged to abolish.

Energy Secretary James B. Edwards will appeal some of the proposed cuts at a meeting Monday with the White House budget review board, whose members are OMB Director David A. Stockman and presidential aides Edwin Meese III and James A. Baker III.

DOE originally sought $14.4 billion in budget authority, but OMB directed the department to lower that by $2 billion to $3 billion. DOE obliged, reducing its request to about $12.5 billion including spending for the strategic petroleum reserve. OMB then slashed another $3 billion for the proposal.

Congressional sources confirmed the magnitude of the proposed cuts, many of which were made public by the newsletter Inside Energy.

If OMB prevails and President Reagan seeks essentially to eliminate the solar, fossil fuels and conservation programs, he will meet major opposition on Capitol Hill. In conservation, for instance, Congress is on the way to appropriating more than $400 million for 1982, compared to the $172 million sought in Reagan's latest budget requests.

Reagan's revisions last February to the Carter administration's 1982 budget included projections of much higher spending for solar, fossil fuels and conservation programs than the latest OMB proposals. Instead of the total of $770 million foreseen in February for the three in 1983, OMB now wants less than $200 million.

Money for the strategic petroleum reserve would be cut by about one-third from this year's level of $3.4 billion. Since most of the money goes to buy oil for the reserve, the administration must intend to reduce the rate at which it is to be filled.

Many of the cuts in the nuclear area involved shifting the burden from the government to utilities in dealing with spent fuel from reactors used for generating electricity. However, among the other cuts was elimination of money for a second-generation breeder reactor that was supposed to follow construction of the Clinch River facility.