DOES BIG OIL HAVE such a stranglehold on most of the nation's large law firms that it is almost impossible to mount a major suit against the industry giants?

That is the question raised by Westinghouse Electric Co. in a Chicago federal court after the first two firms it picked to run a multimillion-dollar price fixing suit against 29 uranium producers, including at least three major oil companies, were forced to withdraw because they previously had represented petroleum companies.

"The oil companies are so litigious that they are always in court. To find a large law firm that hasn't represented an oil company at some time is almost impossible," a Westinghouse official said. He was paraphrasing comments made to U.S. District Judge Prentice Marshall in Chicago by Lee A. Freeman Jr., a Westinghouse lawyer there.

The saga of Westinghouse's attempts to find legal counsel in this case illustrates the complexity of the modern corporate law practice, in which industrial giants employ a host of law firms and law firms themselves have gotten so large they need computers to tell them if a new client may cause a conflict of intrest.

It's not that Westinghouse has been without lawyers in this case. Company officials feel they have been well represented by Freeman, the senior partner of the small Chicago firm of Freeman Rothe.

"He's one of the best," said a Westinghouse spokesman. "But it's a question of resources."

In a case as complex as this, Westinghouse feels it needs a leading law firm with computers, paralegals and dozens of backup attorneys to research all possible points of law - something a small firm such as Freedman Rothe does not have.

Westinghouse first hired Kirkland & Ellis, a Chicago firm, to press the suit. But three oil companies among the 29 defendants in the suit - Gulf, Kerr-McGee and Getty - argued that the firm's Washington office represents the American Petroleum Institute to which they belong. They said information gathered while working for API might be used against them in the suit.

Judge Marshall agreed, and gave Washington a choice: fire Kirkland & Ellis, to which it had already paid $2.5 million in legal fees, or drop charges against the three oil firms. Westinghouse fired Kirkland & Ellis, and next picked the Cleveland-Washington firm of Jones Day Reavis & Pogue.

Westinghouse ran into trouble there, too. Jones Day had represented at least six of the defendants in the case in other, unrelated, matters. Moreover, two lawyers who had just joined the firms Washington office - Donald I. Baker, a partner, and Jonathan C. Rose - had been top officials in the Justice Department's antitrust division during an investigation of uuranium price fixing involving the same defendants.

Even though both Baker and Rose swore they took no part in the government investigation and the firm promised to isolate them from fees and information in the case, Judge Marshall indicated he saw conflict problems and the three oil companies filed formal objections.

Last week, Westinghouse settled on new laywers - Donovan, Leisure, Newton & Irvine, New York's fifth largest law firm with 185 attorneys.

The firm's senior partner, George S. Leisure Jr., had represented Westinghouse in another of the tangled skein of suits arising from the electric company's move into the uranium business.

Donovan Leisure was last in the news when a partner - who later resigned - admitted lying a sworn statement about the destruction of documents in a case which the firm's client, Eastman Kodak, was charged by Berkey Photo Co. of illegally monopolizing the amateur photographic market.

As a result of the disclosure in the final days of the six-month trial, Donovan Leisure was fired as the attorney for the appeal. Moreover, Kodak is expected to try to reverse the $113 million antitrust judgement by arguing that serious errors were made by its lawyers - Donovan Leisure.

Washington lawyers will have their last chance to comment on the proposed new D.C. Bar rules to curb the revolving door between government and private practice before the Bar's board of governors considers them at its Oct. 17 meeting. Comments are due by Sept. 27.

The proposal from the Bar's Legal Ethics Committee is printed in the August-September issue of District Lawyer, the Bar's official publication.

Here's a case of one government agency criticizing another in public. The Justice Department's antitrust division told the Internal Revenue Service that it hasn't gone far enough in allowing lawyers who practice before it to advertise.

"We would like to express our regret that the proposed rules neither affirmatively support the concept of advertising nor encourage its use as a means to inform the public of the availability and cost of tax-related services," the Justice lawyers said in a letter similar to ones they have written to the American Bar Association and state supreme courts criticizing restrictions on lawyer advertising.

Short takes: Washington lawyer Robert Ellis Smith's upcoming book, "Privacy: How to Protect What's Left of It," contains a dig at gossiping lawyers and doctors. "At a cocktail party or on the golf course," he wrote, "an attorney or doctor is often lax about protecting the privacy of a patient or a client."

The Richmond firm of Franis, Hubbard, Tice & Warren now takes credit cards . . . Looking for a job? The Legal Services Corp. is running a meeting here Sept. 14-16 to tell experienced attorneys about possible openings in the corporation's expanding neighborhood legal services programs for the poor across the country . . . Federal Bar Association holding its annual convention Sept. 12-15 at the Mayflower hotel here . . . Thomas E. Kane, a former consultant in ocean law with the North Carolina Attorney General's office and an attorney-analyst with the Library of Congress' Congressional Research Service, going into private practice with offices here and in Raleigh, N.C.