House Republicans, in their first leadership shake-up since 1980, unanimously elected Rep. Dick Cheney (Wyo.) as chairman of the Republican Conference yesterday.

Cheney, White House chief of staff under President Gerald R. Ford, succeeds Rep. Jack Kemp (N.Y.), who relinquished the No. 3 leadership post to concentrate on his bid for the Republican presidential nomination. Cheney's previous position as head of the GOP Policy Committee was taken by Rep. Jerry Lewis in a close contest with one of his California colleagues, Rep. Duncan L. Hunter.

In a three-way race to succeed Lewis as head of the House Republican Research Committee, Rep. Mickey Edwards (Okla.) prevailed over Reps. Steven Gunderson (Wis.) and Steve Bartlett (Tex.).

The changes do not indicate any fundamental philosophical shift in the House Republican leadership, but they do position a new generation of younger Republicans for the challenge of directing the minority party in the post-Reagan era.

Although Cheney and Lewis are conservatives, they, with Edwards, tend to be issue-oriented consensus-builders who are more inclined than some other Republican conservatives to build coalitions with more moderate GOP elements and Democrats.

Lewis' 88-to-82 victory was a narrow rejection of the more confrontational style of Hunter, a member of the Conservative Opportunity Society whose members have aggressively challenged the Democratic majority in the House. The 31-member policy committee maps party strategy and positions in the House, where Democrats outnumber Republicans 257 to 178.

In succeeding Kemp as head of the caucus of all House Republicans, Cheney has positioned himself as a possible heir to Minority Leader Robert H. Michel of Illinois. Michel, 64, intends to seek reelection in 1988, but his plans beyond that are uncertain.

In addition, the Republican Whip, Rep. Trent Lott (Miss.), would likely run for the Senate if his state's senior Democrat, 85-year-old Sen. John C. Stennis, chooses to retire.

Cheney, unopposed for conference chairman, politely dodged questions about his future, saying, "I deal with these races one at a time."

But he promised to work "very aggressively" to help the GOP attain majority party status in the House, something it has not had since the Eisenhower administration.

"One of our tasks is to identify an independent identity as House Republicans," Cheney said.

Cheney and Lewis said they intend to mold House Republicans into a more effective force for determining the direction of the party as it nears the end of the Reagan era and faces a Democratic Senate. House Republicans, promised Cheney, will play a major role in choosing their party's presidential nominee and in shaping the convention platform next year.

Lewis pledged to "reach out to the broad mix" of Republicans in developing the party's positions in the House. "My first goal is to make sure the policy committee attracts broad participation across the spectrum." He said he would frequently appoint task forces to develop GOP policies and would not shy from controversial issues such as AIDS.

"If we are going to work effectively to become a majority, we are going to have to be controversial," Lewis said.