President Reagan is expected to appoint several sharp critics of welfare or hunger relief programs to a new presidential study commission on hunger. They include former governor Edward J. King (D-Mass.) and Dr. George Graham of Johns Hopkins University, sources said yesterday.

Another critic of hunger programs, former House Agriculture Committee chairman W.R. (Bob) Poage (D-Tex.), was asked to participate in the special three-month study of hunger in America but declined, White House sources said.

Two others who are expected to be appointed have been supporters of private programs to feed the hungry.

A philosophical tug of war has erupted within the White House over the purpose of the commission. Aides to White House counselor Edwin Meese III are urging that it focus on administrative shortcomings in federal food programs, sources said. Aides to chief of staff James A. Baker III, however, are pushing for a study of the root problems of hunger in U.S. society, the sources said.

The official list of members of the Task Force on Food Assistance has not been released. However, sources on Capitol Hill and in the administration said the expected members include, in addition to King and Graham:

* J. Clayburn LaForce Jr., dean of the school of management of UCLA, chairman.

* Kenneth Clarkson, associate director of the Office of Management and Budget for human resources from 1982 to 1983.

* John Driggs, former Republican mayor of Phoenix, now a savings and loan executive and also board chairman of Second Harvest, an organization that helps obtain donations nationwide for food banks.

* Sandra Smolley, Republican member of the Sacramento County Board of Supervisors.

* John Perkins of Mississippi, the only black on the list and president of the Voice of Calvary Ministries, an evangelical church.

* Betsy Rollins, director of a soup kitchen at St. Phillip's Episcopal Church in Durham, N.C.

Sources said there will be several other members, but their names are not known.

Documents obtained by The Washington Post indicate that a number of the potential members have been sharply critical of federal programs in the past.

King was a critic of cash welfare programs and was viewed as supporting Reagan's program cuts.

Graham in 1981 called the popular women-infant-children feeding program (WIC) "wasteful and unneeded," and said in a letter to Vice President Bush that he was collaborating with OMB in drafting reasons for cutting it.

Last April 6 Graham told the Senate Agriculture Committee that "the nutritional status of our people including low-income groups is very good and continually getting better" and that "the greatest threat to their health lies in overnutrition."

Clarkson, in a 1975 book, called the food stamp program a "failure" and said perhaps it should be abolished in favor of programs that serve the same ends better.

Perkins, described as a former black activist and one-time board member of Bread for the World, wrote in a 1976 book that "the welfare system is one of the most wasteful and destructive institutions created in recent history."