Former Federal Trade Commission Chairman James C. Miller III was sworn in yesterday as the new director of the Office of Management and Budget, where he'll be working with three former FTC bureau directors and its general counsel.

The day before, President Reagan named FTC Commissioner Terry Calvani as acting FTC chairman until a successor to Miller is nominated and confirmed. Calvani, 38, a former law professor at Vanderbilt University and a member of the commission for almost two years, moved quickly to fill some of the vacant slots:

*Timothy J. Muris, who had directed the FTC's Bureau of Competition, becomes executive associate director of OMB, while Walter T. Winslow, the bureau's deputy director, becomes acting director. Muris worked at OMB as an assistant to Miller when Miller was head of OMB's Office of Information and Regulatory Affairs.

*ecomes associate director of OMB for economics and government. Amanda Pedersen, the bureau's deputy director, becomes acting director.

*Wendy Lee Gramm, who directed the Bureau of Economics, takes over Miller's old job as administrator of the regulatory affairs office. David T. Scheffman, deputy director of the bureau, will serve as acting director.

*Former FTC general counsel John H. Carley becomes counselor to the OMB director. Mary Tiffany, executive assistant to the chairman, becomes acting general counsel.

*Jeffrey A. Eisenach, formerly special adviser to the FTC chairman for economic policy and operations, becomes executive assistant to the OMB director.

Karen Johnston, the FTC's director of congressional relations, is also leaving the FTC, but not joining the exodus to OMB. Johnston plans to leave Washington at the end of the month to work on the campaign of Rep. James T. Broyhill (R-N.C.) for the North Carolina Senate seat of Republican John P. East. She will be working alongside her husband, former Rep. Eugene Johnston (R-N.C.), who will serve as Broyhill's finance chairman.

Johnston previously had said she would stay on until Congress passed a bill reauthorizing the FTC, but she said yesterday that the bill is not expected to pass before her departure Nov. 1. But a House-Senate conference is expected before the end of the month, she said, and a final bill is expected to pass by the end of the congressional session.

Calvani has named one of his attorney advisers, Randolf W. Tritell, to serve as his executive assistant. Calvani also named three special assistants: Neil W. Averitt, former attorney adviser to former Commissioner George W. Douglas and former special assistant to Miller; Donald S. Clark, a former attorney adviser to Douglas; and Cynthia E. Smith, an attorney from the agency's Atlanta regional office.

Calvani's appointment may be a sign that the White House will not move quickly to nominate replacements for Miller and Douglas, a conservative Democrat who left the commission last month to return to Texas.

The president is expected to nominate Agriculture Department general counsel Daniel Oliver and Kenneth Elzinga, a University of Virginia economics professor, to fill the seats of Miller and Douglas, respectively.

Oliver, a Republican, also served as general counsel of the Education Department and is a former executive editor of National Review, as well as a former director of the American Conservative Union Inc. Elzinga, an independent, is an antitrust expert who writes mystery novels on the side. From 1970-71, he served as special economic adviser to the assistant attorney general for antitrust and from 1971-79 as a member of the Nuclear Regulatory Commission's Atomic Safety and Licensing Board Panel.

Although agency and congressional sources say the administration is close to a decision, Crawford, Muris and Gramm have also been mentioned as possible nominees.

WAITING GAME . . . Rep. James J. Florio (D-N.J.), chairman of the House Energy and Commerce subcommittee on commerce, transportation and tourism, is still waiting for answers from the FTC to his questions about Gulf Corp.'s divestiture of certain assets in the Southeast.

In a Sept. 4 letter, Florio asked the agency to respond to complaints from gasoline retailers about the FTC's review of its consent agreement approving Chevron Corp's $13.2 billion takeover of Gulf. The agreement required the divestiture of 4,000 gas stations, including "the Gulf brand name and trademark." The retailers have complained that despite that, the FTC later approved the sale of Gulf stations that had only a temporary license to the Gulf trademarks. Florio requested a reply by Oct. 4, but his staff said yesterday that he has not yet received one.