Gen. Edward Charles Meyer was sworn in yesterday as Army chief of staff, completing the new team President Carter has chosen to run the military services and advise him on such key issues as the strategic arms limitation treaty (SALT II) and a "quick strike force" for possible use in the Persian Gulf.

Carter, since taking office in 1977, has had the opportunity to replace every member of the Joint Chiefs of Staff who, by law serve for four years. Gen. George S. Brown, former chairman of the joint chiefs, died Dec. 5. The other vacancies on the joint chiefs result from completed tours of duty.

The 50-year-old "Shy" Meyer is the youngest member of the chiefs. He was graduated from the U.S. Military Academy in 1951 and was in combat during the Korean and Vietnam wars.

At a swearing-in ceremony yesterday at the Pentagon, Defense Secretary Harold Brown said Meyer's job as head of the 750,000-member Army "will be difficult because there is a great deal of change to be made with limited resources."

The Army, partly because it needs more people than any other service, is having the hardest time of any service in filling its ranks with volunteers. It also is so short of reserves that a number of untraditional measures, including drafting veterans, are under consideration at the Pentagon.

Meyer said yesterday that "the Army is to be judged against our ability to go to war" so it will not have to go to war at all.

Besides Meyer and Marine Commandant-designate Robert H. Barrow, 57, Carter's new military team consists of Air Force Gen. David C. Jones, 57, chairman of the joint chiefs; Adm. Thomas B. Hayward, 55, chief of naval operations, and Gen. Lew Allen Jr., 52, Air Force chief of staff.

Carter is counting heavily on his team of military leaders to help win Senate approval of SALT II. Sources said the chiefs expressed their unanimous endorsement of SALT II in a letter sent to the president last week shortly before he flew to Vienna for the treaty signing ceremonies.

Besides counting on the chiefs for help on SALT II, Carter is looking to them to recommend ways to provide the United States with more leverage in the Third World. It is in this context that the Army is drafting plans for a quick reaction force, fully armed and with support units designated to go along with it, which could respond to crises in crucial areas like the Persian Gulf. CAPTION: Picture, Gen. Edward C. Meyer gets a helping hand after one of his stars fell from his shoulder during swearing-in. By Frank Johnston - The Washington Post