Frustrated by their inability to win congressional support for an oil import fee, some oil industry executives have decided to try another route to financial relief: U.S. trade law.

An industry group led by Enserch Corp. is preparing to petition the International Trade Commission contending the domestic oil industry has been seriously injured by increased imports of crude oil and is entitled to five years of "temporary relief" in the form of quotas or tariffs.

"We are moving ahead with deliberate speed to put us in a position to file by late July," Enserch spokesman Candy Hooper said.

The oil petition will cite the same provision of the 1974 Trade Act that Harley-Davidson Inc. invoked to win tariffs on imported motorcycles while the company regrouped to meet stiff Japanese competition.

The provision apparently has never been used to protect a commodity such as oil, and the prospect got a cool reception this week from Energy Department officials.

"DOE does not support a proposal to use the trade act," department spokesman C. Anson Franklin said. "It's another approach to impose an oil import fee and the administration opposes an oil import fee."

The proposal illustrates the rising desperation of the oil industry, which has been largely unsuccessful in persuading the administration or Congress that low oil prices are as bad for the nation as they are for the industry.

President Reagan repeatedly has rebuffed suggestions for an oil import fee to bring domestic prices up. The most recent legislative effort to bolster crude prices came under scathing attack this week by the U.S. trade representative, nearly a third of the Senate and an unlikely coalition of industry, environmental and consumer groups.

Against that backdrop, Enserch officials believe they have nothing to lose -- and perhaps quite a bit to gain -- by trying to take the matter out of the realm of domestic politics and transforming it into an issue of international trade.

As a strategy paper prepared for Enserch puts it: "If these proceedings are successful, the potential payoff for the industry is enormous." The remedy sought by the trade petition is $25-a-barrel domestic oil, to be achieved through price floors, quotas or any other measure the ITC and the president deem appropriate.

If the ITC accepts the petition, according to the strategy paper, the industry is guaranteed a public hearing that "would assist in developing a domestic consensus that there is an oil import problem which warrants presidential action."

The petition process also sets deadlines -- six months for the ITC to make a recommendation and two months more for the president to decide whether to grant relief. "In short, the government cannot stonewall or ignore the petition," the paper said. Leaving nothing to chance, the group also intends to file a parallel petition invoking another provision of trade law, which could force the ITC to study whether the oil industry is vital to U.S. national security.

Five presidents have ruled affirmatively on that question, but the group hopes an ITC study "could serve as a fallback authority for presidential relief" in the event that the ITC ruled against relief.

If the effort were successful, it would give the industry even more relief than the provisions Senate Finance Chairman Lloyd Bentsen (D-Tex.) inserted in a trade bill that is expected to come before the Senate next week. That legislation has formidable opposition -- another reason the oil industry is toying with the trade law.

"Bringing these proceedings simultaneously offers the possibility of the government acting to get the price of oil up -- where it needs to be -- without going to Congress," the strategy paper said.

An aide to Bentsen was noncommittal on the Enserch proposal. "We are aware of it," he said. "I don't know that we have an opinion."

Hooper said the firm has enlisted the support of several trade associations, including the Texas Independent Producers and Royalty Owners.