The nation's 16 largest oil companies would collect an extra $1.8 billion to $4.2 billion in the first year if federal price controls were lifted entirely from natural gas, according to unreleased figures compiled by the Energy Department.

The figures, compiled by the Energy Information Administration, spell out for the first time how each of the major oil companies would fare if the Reagan administration succeeded in deregulating natural gas, as it has proposed. Gulf Oil Co. would be the biggest winner. Its first-year gain would be $645 million to $869 million.

The Senate Energy Committee is expected to send a deregulation bill to the floor today.

The 16 major oil companies own 54 percent of the nation's gas reserves.

Sen. Howard M. Metzenbaum (D-Ohio), who has been battling deregulation in the committee and has vowed to filibuster if necessary to block the bill on the floor, obtained a copy of the Energy Department report and made it available to The Washington Post.

An Energy Information Administration official said yesterday afternoon that the report, which was completed about a week ago, "should give people a good idea who the players are and what they are playing for."

Last night, however, Erich Evered, EIA administrator, called the Post to ask that the figures not be published, saying that the report's methodology was faulty and that its conclusions were being revised.

There are basically two kinds of gas under present law, old and new. Old gas comes from wells drilled before 1977, and its price is tightly controlled; new is allowed to drift up toward market price levels.

The administration has said that while old gas prices would rise under its proposal, new gas prices would fall, cutting into the gains of producers.

But the new Energy Department statistics show that the major oil companies have much more old gas than new. Thus the major oil companies mostly would be net winners under the administration proposal, while the major independent gas producing companies and several major interstate pipelines that are more dependent on new gas would lose.

Transco Inc., for example, one of the two pipelines that serves Washington Gas Light Co., would lose between $3 million and $45 million in the first year following decontrol on gas produced by its affiliated companies.

That range and all the ranges in the report depend on assumptions about the state of the gas market and general level of energy prices in the first year of decontrol.

Assuming that the price of all gas under total decontrol stabilized in the current average area of $2.69--a depressed level that most observers say they feel will not last--the revenue Gulf Oil obtains for its gas would increase in the first year by 120 percent.

Gulf would receive an extra $740 million--a 327 percent increase--on sales of its old gas, while receiving $95 million less on its sales of new gas and high-priced gas, according to the government figures.

Phillips Petroleum would be the second-largest winner, netting an additional $262 million.

Mobil would be the third-largest beneficiary, reaping an additional $259 million.

Shell Oil Co., Cities Service Co., Exxon Corp. and Sun Oil Corp. are the other major companies that would gain at least $100 million a year as a result of decontrol.

The only two major oil companies that could be adversely affected by decontrol are Amoco Inc. and Union Oil Co.

But even these stand to gain if the average price after decontrol is $3.20 per thousand cubic feet--which most observers of the gas market say is far more likely--and the other major oil companies would gain even larger profits.