WASHINGTON (AP) _ A government move to win repayment of alleged overcharges by an oil company partly owned by the family of the Reagan administration's No. 2 budget official was delayed by more than two years, a Department of Energy auditor told a Senate panel Tuesday.

William C. Lynch, a supervisor in the department's enforcement office, testified that an order seeking $12 million in alleged crude oil overcharges by Canal Refining Co. was approved by government attorneys in January 1983, but was not actually issued until April 1985 - after congressional investigators began looking into the case.

Canal, of Church Point, La., is a wholly owned subsidiary of Anchor Gasoline Corp. of Tulsa, Okla. Anchor's chairman is Joseph Wright Sr., the father of Deputy White House Budget Director Joseph Wright Jr.

The value of the younger Wright's 3 percent ownership in the companies has been put at between $550,000 and $750,000.

Tuesday's hearing by the Senate Governmental Affairs Committee was the third held by a congressional committee into the department's dealings with Anchor and Canal.

Earlier this year, the Wall Street Journal reported that the younger Wright had called the Energy Department's former chief oil pricing enforcer, Rayburn Hanzlik, on Sept. 23, 1982, about a separate case alleging $7.4 million in violations against Anchor.

Wright has since denied that he tried to improperly influence the government's cases against the two companies. He said he was only trying to get Hanzlik to meet with Anchor officials over their complaints about dealing with the department's Kansas City regional office, which was in charge of the $7.4 million Anchor case.

Wright, along with Hanzlik, was scheduled to testify before the Senate committee on Wednesday.

Before any witnesses were called at Tuesday's hearing, Democrats on the Senate committee charged that Wright had asked Hanzlik to ''fix'' the case, and that Hanzlik complied with him.

''Mr. Wright found that his family business was charged with violating the law and was being directed to repay millions of dollars,'' said Sen. Albert Gore Jr., D-Tenn. ''Essentially, he asked Mr. Hanzlik to fix the case. Mr. Hanzlik cooperated in fixing the case.''

Sen. Thomas Eagleton said Anchor was formally notified of its alleged $7.4 million violation on Sept. 14, 1982 - just nine days before Wright called Hanzlik.

''It has been more than three years since the charges were filed,'' he said. ''Yet, even as we sit here today, the case against Anchor is still unresolved. More than two years after the initial charges against Canal were prepared for filing... it, too, is unresolved.''

Eagleton added: ''If this were a fix, those who sought to profit from it should not be allowed to succed.''

Republicans on the committee agreed that it was improper for Wright to have ever contacted Hanzlik. But they said Wright should have an opportunity to present his case.

''Before we hang Mr. Wright, I think we ought to have a trial first,'' said Sen. William Cohen, R-Maine.

Lynch said he spent more than two years trying to get Milton Lorenz, the Energy Department's chief counsel, to approve an order directing Canal to repay the $12 million plus another $8 million in interest.

He testified that Lorenz never gave him a reason why it was not approved, even though the case ''was the simplest entitlement violation that one could pursue.''

Lynch also complained that Lorenz gave a copy of the proposed draft violation order to an attorney for Canal and Anchor in January 1983.

''We never do that,'' Lynch said. ''In the 100 pending entitlement cases we were handling at that time, I know of no other case in which that was done.''

Lorenz also is scheduled to testify Wednesday.