Despite all the adverse publicity, the Teamsters union still has a lot of clout in Ronald Reagan's Washington.

A case in point is the nomination of Charles L. Woods, a $69,200-a-year Teamsters official from California, who was picked to fill a vacancy on the National Mediation Board. The Senate Labor Committee recommended his confirmation yesterday without discussion despite grumblings from the airline industry.

"There's no question that Teamsters have to be appointed from time to time," said Sen. Orrin G. Hatch (R-Utah) when asked about reports that the nomination stemmed from Teamsters President Jackie Presser's support of President Reagan in the last two elections. "The Teamsters have a right to be represented" in government.

The three-member mediation board presides over labor disputes in the railway and airline industries. Under its statute, "no person in the employment of or who is pecuniarily or otherwise interested in any organization of employes or any carrier shall enter upon the duties of or continue to be a member of the board."

Woods, 70, has been a Teamsters airline representative for 10 years. Before that, he was a United Airlines pilot for 28 years and an active member and national unit chairman of the Air Line Pilots Association (ALPA). He receives $51,986 a year in airline pensions.

Reagan administration and airline industry sources said Woods' nomination originated with "a recommendation from the Teamsters." Woods said he believed one of the first letters supporting him was written to Reagan by Presser.

"It wasn't something I sought myself," Woods told a reporter.

Several airline industry officials have protested that board members, who are paid $72,300 a year, should be independent and not from the ranks of union or management in the air or rail industries.

"Simply stated, we think a contrary policy compromises the neutrality of the agency," James E. Conway, an official with the Airline Industrial Relations Conference, wrote to Sen. Don Nickles (R-Okla.), chairman of the labor subcommittee. Conway later added that "at a minumum," Woods should disqualify himself from all cases involving the Teamsters or ALPA.

Woods declined, saying he could be a neutral arbiter and would decide whether to disqualify himself on a case-by-case basis.

Hatch said he was satisfied by Woods' pledge to quit the Teamsters before being sworn in and to "sever all ties" to the union, "financial and otherwise," except for a $585-a-month pension. Hatch and committee lawyers said they did not interpret the law as prohibiting direct transitions from affected unions or industries to the board.

Woods did pledge to disqualify himself "from any case or proceeding in which I participated personally during my Teamster employment," including a prolonged union representation dispute with Continental Airlines that is now before the board. In future cases, he said he would make "full disclosure to all parties and entertain formal motions for recusal."

Clark Onstad, Continental Airlines vice president for governmental affairs, charged that the nomination represented "an emerging attempt by the Teamsters to organize more and more people in the airline industry."

The Teamsters represent about 30,000 airline workers, according to the mediation board. The Continental case could add several thousand more.