The president and Mrs. Reagan began a marathon of ball-giving last night with a visit to the American Legion's banquet in a capital celebrating both the inauguration and the hostages' freedom.

The old Glenn Miller band struck up "Moonlight Serenade" and President and Mrs. Reagan danced their first dance of the evening on stage at the Pension Building last night to the cheers of nearly 5,600 ballgoers.

The Reagans arrived a little ahead of schedule at 11:05 p.m. bringing news that "our prisoners of war," as Reagan described the 52 American hostages, are "healthy and sound." That and the news that the Christmas tree on the Ellipse had been lit for the first time since Christmas 1979 got another cheer.

In the crowd were most of the foreign chiefs of mission in Washington, many of them struggling to get to former secretary of state Henry Kissinger. At one point a fistfight nearly broke out behind the Kissingers' box when a disgruntled ballgoer tried to evict an unidentified ambassador from his box. Fearing a fight might erupt, Nancy Kissinger began screaming for "Jerry, Jerry," her husband's bodyguard.

There was more commotion with the arrival of Secretary of State-designate Alexander Haig and wife Pat.

"Come into our box, Al," Kissinger invited. "I just threw somebody out of this box, and I had no right to be in it myself."

Asked by a reporter what the official U.S. attitude on Iran will be now that the hostages have been freed Haig looked a little startled.

"What's your suggestion?" he asked, then added, "We'll have to decide that when we see how everything goes."

When asked the same question, Kissinger didn't hesitate an instant. "I'm going to stay quiet for about three months and let Haig do his own thing," he said.

Did that mean that he knew what to do, his questioner persisted.

"If there's anything self-serving or egotistical to be said," Kissinger replied, grinning. "you know that I'll say it."

Secretary of Defense Caspar Weinberger arrived to find the box he had been assigned filled with the ambassadors and their wives from the Ivory Coast, Morocco and Egypt as well as Helga Orfila, wife of the OAS Secretary-General Alejandro Orfila. Within a few minutes a newcomer laid claim to the box and everybody but Weinberger and his wife found themselves being thrown out.

The exiting diplomats looked a little sheepish but apparently decided against creating a scene or an international incident.

"We were hysterical," said Helga Orfila, trying to keep from laughing.

Nancy Reagan's gown -- the glittering white one-shoulder original created for her by Galanos -- aroused almost as much comment as her new coiffure. With her hair pulled back from her face and secured in a twist, some of the partygoers said she was stunning -- but almost unrecognizable.