The U.S. Supreme Court agreed yesterday to determine whether a Washington man awarded workmen's compensation benefits under Virginia law could apply for benfits in the District, where he was injured seriously in 1971.

The worker, Halley I. Thomas, was injured in Arlington while operating an air hammer for Washington Gas Light Co. and has been unable to work since that time.

After being granted benefits in Virginia, Thomas sought D.C. compensation instead, but Washington Gas has fought those attempts in a series of administrative and court challenges.

A Department of Labor law judge ruled that Thomas was entitled to D.C. benefits even though the accident took place in Virginia.

Washington Gas fought the case, ultimately appealing the decision to the 4th Circuit U.S. Court of Appeals, where the decision was overturned.

The Supreme Court will hear oral arguments this term on Thomas's appeal of the lower-court ruling.

But under Virginia law, Thomas' benefits ran out in October 1978, after he had been awarded $24,800, the maximum compensation under state law. Under D.C. law, the benefits could be continued so long as Thomas suffered from the disabling injury.

Thomas said in an interview that he had been in and out of the hospital "six or sven times" since the injury and said he was being supported by his wife and Social Security benefits.

If granted the right to D.C. benefits, Thomas, 36, would be entitled to continuing compensation and a larger sum, which would be indexed and would have been more than the $62 a week he claimed under Virginia law.

Thomas asked the Supreme Court to determine whether a worker can receive these benefits from more than one jurisdicton for a single injury.He was awarded temporary total disability in Virginia and permanent total disability in D.C. The appeals court overturned the latter award.

A spokesman for Washington Gas said the company "fully complied" with workmen's compensation laws in Virginia.

The Associated Press also reported the following actions by the high court:

The Supreme Court agreed to decide whether the state of New York violated the rights of electric utilities by ordering them to halt promotional advertisements.

The justices said they will study arguments by Central Hudson Gas & Electgric Corp. that the state Public Service Commission violated its free speech rights in imposing the ban after the 1973 oil embargo. State courts have upheld the PSC action.

The court also agreed to review rulings the government said could ruin many Indian-owned road construction companies by requiring that road contracts be awarded only after competitive bidding.

In other actions affecting business, the Supreme Court:

Agreed to review Wisconsin's practice of taxing major corporations as "unitary businesses," a practice Exxon Corp. contends forces it to pay tax on earnings from outside the state. Exxon is appealing a $316,475 tax assessment for the years 1965 to 1968.

Refused to hear a claim against McDonald's Systems Inc. in which Louis Martino of Ottumwa, Iowa, claimed McDonald's violated antitrust law when it took away Martino's franchise because his relatives bought a franchise for a competing fast-food chain. Lower courts dismissed the case on procedural grounds.

Rejected the United Methodist Church's attempt to free itself of $371 million in lawsuits filed as a result of problems with church-related retirement homes and convalescent hospitals. Church lawyers claimed that as an unincorporated entity the church could not be sued.

Agreed to decide whether the federal courts have jurisdiction in a suit brought by the trustees of Fidelity Mortgage Investors, a real estate investment trust based in Florida, against Navarro Savings Association of Corsicana, Texas. The suit claims the savings association defaulted on a promissory note of $850,000, but has been stymied on the question of whether the suit could be filed only in Texas state courts.