The oil industry tried a second time yesterday to keep for itself part of President Carter's proposed wellhead tax on oil, offering to team up with shivering New Englanders and Southern farmers. The New Englanders and farmers got what they wanted, but the industry lost in actions by the House Ways and Means Committee.

The committee rejected, 20 to 17, a proposal to give oil producers $5 billion of well head tax collections by 1981 provided they use it to look for new oil. Oil supporters tried to push attaching it to a special revenue rebate for users of home heating oil in the Northeast and rural users of propane.

The committee voted a rebate for home heating oil users, and an exemption from the tax residential or agricultural use of propane, and then nailed the oil tax and rebate into the tax part of President Carter's energy bill.

The oil tax is a key part of the President's program to save oil and reduce dependence on imports. He would impose a three-stage tax that would push the price of crude oil up to world levels in hopes this would reduce consumption. To prevent windfall profits to producers and since the purpose in not to raise revenue, the President has proposed that the tax revenues be rebated to the people. He hopes they would use it to buy something other than oil.

The tax would be paid not by producers but by the "first purchaser," the refiner. The administration strongly opposed giving part of the proceeds to producers as a "ripoff on the American people."

Under Carter's plan most of the revenue would be given back to taxpayers by lowered withholding of tax collections from weekly paychecks. Because some sections of the country can't get natural gas and must heat homes with oil, the President proposed a special rebate to them, which would be paid to retail dealers and handed on to customers as three-or-four-cent per gallon reductions in their heating bills.

Two weeks ago when Ways and Means took tentative votes on the oil tax, it voted to approve the tax and a rebate to taxpayers of about $28 apiece per year - twice for a family - but it voted to kill the home heating oil rebate, as a special preference for one region of the country. And it rejected a 20 per cent plowback by 21 to 16.

Northeast members grumbled that they had better get their rebate when the final vote was taken or they would try to kill the oil tax. It appeared clear when the final vote came yesterday that arrangements had been made. Rep. Jim* Guy Tucker (D-Ark.) fashioned an amendment that gave special treatment to users of propane and home heating oil. This was approved, 21 to 0, with several leading members of the committee who voted earlier against the special rebate now switching to support it. The plowback was then killed. The only member switching to support the plowback yesterday was Rep. Ken Holland (D-S.C.).

These actions reduced the amount available to be rebated to taxpayers to about $22 a year, or $44 for each family or head of household. The committee approved the rebate for next year only and must decide later what to do with it in the future.

Meanwhile, the House Commerce Committee met to begin consideration of nontax parts of the Carter energy package drafted by a subcommittee headed by Rep. John D. Dingeii (D-Mich). After a day of parliamentary wrangling the committee adjourned after deciding only that the first vote will come on the crucial issue if removing federal price controls from natural gas.

Backers of the President's proposal to keep controls but raise the price want to get this explosive issue behind them before recessing for 10 days this weekend. They feared that members would get worked over by supporters of deregulation at home.

Some members said the issue is so close in the 43-member committee it may be decided by the margin of one vote.

Dingell's subcommittee voted 12 to 10 to deregulate the price of new natural gas. The administration has said this could cost consumers an extra $10 billion a year by 1985. The President wanted to extend regulation from gas flowing across state lines to gas consumed within the state where produced. But he would raise the regulated price to $175 per thousand cubic feet from its present level of $1.45.

The House Government Operations Committee approved, 22 to 11, another piece of Carter's energy package - a provision authorizing the government to buy 6,000 10-passenger vechicles to carry paying government workers to and from work to save gasoline. Rep. Paul N. McCloskey (R-Calif.) objected to the proposal as "a new federal employees' benefit plan."