A House-Senate conference committee last night approved a compromise version of President Carter's proposed crude oil tax, paving the way for final passage by both houses sometime next month.

Approval came after the conferees resolved a last-minute snag over which congressional committees should handle a new program in the bill to help low-income families meet rising energy costs.

Carter has indicated he will eagerly sign the legislation, which he proposed last April to tax back some of the extra money oil companies will make because of his decision to lift oil price controls.

The legislation would raise $227.7 billion from oil producers over the next 11 years and spend the money on new energy production, mass transit, aid to the poor and possibly a small tax cut.

The bill also contains a new tax break for so-called "small savers" and $9.2 billion worth of tax credits for homeowners and businesses that buy equipment intended to save or produce more energy.

And, undoing a "reform" that Congress passed in 1976, the bill would cut capital gains taxes on profits from the sale of inherited property.

Yesterday's action marked a major victory for the president, who has made the crude oil proposal a centerpiece of his legislative program.

The compromise is almost exactly halfway between the tax Carter proposed, which was approved almost intact by the House, and a substantially weaker version passed by the Senate.

Carter's original plan would have cut by 64 percent the estimated $442.4 billion in extra revenues that the oil companies would receive -- after federal, state and local taxes -- as a result of price decontrol.

The Senate version of the measure would have trimmed producer revenues only 38 percent. Yesterday's compromise would cut the oil companies' take by 50 percent, leaving them with $221 billion over the 11-year period.

The crude oil tax is the major element in a three-part energy plan Carter has proposed. The two other pieces -- a crash program to develop synthetic fuels, and a plan to cut red tape on energy projects -- are bogged down in separate conference committees.

The plan to aid low-income families approved by the conferees yesterday would provide $3.1 billion in cash grants this year and next and substantially more in later years, primarily to help offset rising energy prices.

The money would be channeled through the states in 1980 and 1981, but later would be distributed directly by the federal government as part of the Supplemental Security Income program.

The $227.7 billion the crude oil tax would raise between now and 1990 would come primarily from the major oil companies, which would pay about $205 billion. Smaller, independent producers would be taxed about $23 billion.

Oil produced by states, Indian tribes and charitable institutions that own wells would be exempt entirely. The conferees earlier had voted to tax Indian tribes' oil at a 30 percent rate, but reconsidered after heavy lobbying.

Under the plan contained in the compromise, the money would be spent this way:

25 percent, or $56.8 billion over the full 11 years, would go for aid to low-income families to help them cope with soaring energy prices. The panel scrapped a Senate-passed tax credit for purchases of home heating fuel.

15 percent, or $34.1 billion, would go for mass transit grants, railroad rehabilitation and other government-loans and loan guarantees to encourage energy conservation and development.

The conferees also voted informally to set aside the remaining 60 percent -- amounting to $136.4 billion -- for possible income tax cuts for businesses and individuals, but that move was largely symbolic.

For one thing, the reductions would not take effect unless Congress passed separate tax-cut legislation anyway. And any cuts would be modest: A single $11 billion tax cut continued for the full 11 years would use up $121 billion.

Other elements include:

A so-called "small savers' tax incentive" that would allow all investors to escape taxes on their first $200 in income from interest and dividends -- $400 for married couples -- beginning next Jan. 1. The proposal would cost $4.3 billion over two years.

Interest income currently is taxed the same as wage and salary income, while dividend income is eligible for an exclusion of $100 for single taxpayers and $200 for those filing joint returns.

$9.2 billion worth of tax credits -- $600 million for homeowners and $8.6 billion for businesses -- for energy saving or producing equipment including solar, wind or geothermal power and gasohol production facilities.

The maximum tax credit for installation of solar, wind or geothermal equipment will rise to $4,000 a year, from the current $2,200, retroactive to last Jan. 1. Carter had proposed about $5 billion in energy tax credits.

The levy on oil producers actually an excise tax, would not be imposed uniformly but would vary according to when and where oil was discovered and the size of the firm that produces it.

The tax formula is designed to tax companies on the difference between the oil price in effect when Carter decided to lift controls and the market price at any given time -- a difference that Carter has described as a "windfall."

For large oil companies, the tax rate would vary from a high of 70 percent, for oil discovered before 1979, to 60 percent for small so-called stripper wells, and 30 percent for oil discovered after 1978.

Smaller, independent oil producers would be taxed at much lower rates. So would most Alaskan oil, produced after 1978, which is plagued by high transportation costs. There also are other, more minor exemptions.

Under the plan approved yesterday, the crude oil tax would begin March 1 and would expire sometime between late 1990 and late 1993, depending upon how rapidly oil prices rise between now and then.

Carter had asked that the tax take effect last Jan. 1, but experts said the earlier date would have posed administration problems. The new version will include a tighter formula for computing the base prices to make up the difference.