A $38,000-a year government computer expert has been accused of acincluding trips to Washington Redskin games and more than 200 free lunches from a company with a $7.5 million contract he supervised.

Edwin B. Parker III, a former federal computer manager, alleged received the favors, some of which he also claimed on his expense account, from On-line Systems, a Pittsburgh-based computer firm over a 23-month period. The company's no-bid contract with the Department of Health, Education and Welfare increased $6.5 million during the period.

Parker was given a dismissal notive Monday, and the contract award is under investigation by both the U. S. attorney's office in Washington and the HEW inspector general, sources said yesterday.

"The basis for the investigation is gratuities or irregularities concerning the award of the contract." HEW spokesman Robert Wilson said.

In a letter from John Ellis, executive deputy U. S. commissioner of education, Parker was told he has 30 days to appeal the accusatioN, or lose his job, spokesman said. He was reassigned May 16 from his post as manager of computer operations for the government's student loan program after investigators raised questions about the alleged favors.

HEW officials refused to provide a detailed account of the alleged freebies, but sources indicated some of the more than 200 meals in question were purchased by Gilmore S. (Bim) Wheeler, president of an On-line subsidiary, at expensive restaurants in Washington and elsewhere. The dismissal letter accused Parker of claiming travel expenses for some of the same meals.

Wheeler, son of the late chairman of the Joint Chefs of Staff, Army Gen. Earle G. Wheeler, is a longtime friend and coworker of Parker. He has worked as a $250-a-day consultant on the student loan project that Parker managed. Neither he nor other On-Line officials in Pittsburgh could be reached yesterday.

A spokesman in the firm's Silver Spring office said Wheeler is president of Business, Industry and Management, Inc., which was described as an On-Line subsidiary.

The irregularities allegedly took place between June 27, 1975, when On-Line was awarded its first $1 million contract, and mid-May of this year. Apparently, there is no dispute over how the company provided its services, only if Parker violated HEW's code of conduct in accepting gratuities.

Parker refused comment yesterday.

On-Line Systems is a fast-growing computer program company, which was recently signed a $3.1 million-a-year no-bid contract to provide mailing services for the U.S. Senate.