Government funds available for energy conservation and assistance programs will increase dramatically throughout the Washington area soon as a result of the federal government's distribution of $2.1 billion in overcharge penalties paid last week by Exxon Corp.

Under a formula established by a U.S. District Court order, the District of Columbia will receive $4.6 million, Virginia will receive $53.3 million and Maryland more than $36 million.

The funds must be used for federal energy programs for conservation and assistance to low-income persons. Officials in the District and state governments said they have not yet developed specific plans for spending the money.

The U.S. Department of Energy had alleged that between 1975 and 1981 Exxon charged its customers $895.5 million more than allowed by federal regulation by improperly classifying crude oil from a large oil field in East Texas. The Supreme Court in January let stand lower court determinations that Exxon should pay the overcharges plus interest, which brought the total payment to $2.1 billion.

Exxon made the payment to the Energy Department on Thursday.

The total budget for the District's Energy Office for the current fiscal year is $11.3 million, including $7.7 million the city expected to get from the federal government. That figure did not include the $4.6 million windfall from the Exxon case.

In Virginia, the Exxon money coming to the state is approximately equal to this fiscal year's total budget for the energy programs to be affected. Samuel Bird, director of the Virginia division of energy, noted that the new funds do not have to be spent all at once, however.

Maryland Comptroller Louis L. Goldstein, chairman of the board of the Maryland Energy Overcharge Trust Fund, said officials will hold a number of public meetings around the state before deciding how to allocate the money under the various programs.

D.C. City Administrator Thomas Downs said a separate fund will have to be established for the payment to the city.

The states must send the federal government a statement of assurance that the funds will be used for the specified purposes, and the money is to be disbursed Thursday.