The scene was "home on the range" last night on the West Terrace of the White House, as 180 Japanese and American guests sat down with President and Mrs. Carter for an outdoor meal of barbecued buffalo, chicken and suckling pig.

The meat for the state dinner served to Japanese Prime Minister Masayoshi Ohira took 12 hours to cook yesterday, and the barbecue smoke could be smelled blocks away from the White House.It was served with a Texas-style sauce made by Ambassador Robert Strauss, the President's special representative for trade negotiations, and his wife, Helen.

A week ago, Strauss and Ohira were engaged in delicate trade negotiations which came to halt with the two parties far from agreement. But last night it was barbecue diplomacy and the atmosphere seemed sweeter.

A high administration source said that yesterday morning's Carter-Ohira meetings had "an exceptional quality." He quoted Secretary of State Cyrus Vance as saying the session was "without peer."

In his toast to Prime Minister Ohira, Carter said, "This has been one of the most productive days in my whole diplomatic life," adding that the "economic problems are well on the way to being solved."

He recalled that the last time he had seen Ohira was in 1975, when he was a presidential candidate and Ohira was Japan's finance minister. Ohira asked him at that time, "What do you think your chances are?" He recalled, and, "I said, 'The next time I see you, we will be in the White House.' Of course, I never guessed that he would be the prime minister."

He noted with approval that Ohira "comes from one of the southernmost islands of Japan," and praised that country as "a nation of great economic achievement."

He said that he had recently read Prime Minister Ohira's book, and recalled a quote from it saying that, "It is better to correct a wrong then it is to initiate many rights." He said that there was "quite a discussion" of this idea during the dinner, not only with Ohira but with three-time marathon winner Bill Rodgers, Joan Benoit, whom he called "a great female athlete." and actor Peter Falk, "We concluded that to correct wrongs is the mark of a great politician," the president said.

Over coffee later, Carter told reporters that Japanese had made no big concessions on the trade issue during their meetings earlier in the day.

"But we established a mechanism to solve the trade question before the summit." the president said, adding that, "Everybody is very confident that we can solve this. It was almost a stalemate before he came, as you know."

Standing in the Blue Room with Ohira off to one side, the president said he doubted that thier friendship going back to 1975 played a very important part in yesterday's negotiations. "Except that before anyone else knew who I was or cared, Mr. Ohira had set aside an hour just to talk to me. He saw me probably not as a future president." Then, starting to laugh, Carter said. "It was almost a joke [about meeting again in the White House]. He was joking but I wasn't."

Strauss also reiterated that the trade differences had not been solved. Discussing his other role, that of cook, he said that he and his wife had made the barbecue sauce on Sunday. Ohira said the sauce was good, but added that the buffalo meat "was a little coarse."

Bobby Short sang a selection of the popular songs with which he is identified, ranging from Cole Porter to Stephen Sondheim. This kind of repertoire is unusual for a state dinner, which usually has classical music, but Short explained that "Mr. Ohira said he is a great fan of American popular music."

This was his second appearance at the White House as a performer, he said. "I came to play for Nixon, and there was a very brittle atmosphere. The Carters are very easy-It's not casual, but it's easy." It sounded something like a description of his own singing style.

Short first met the Carters at a United Nations dinner in New York, and later came to the White House as an invited guest at a state dinner.

"Now that I've been here as a guest," he said, "coming back, I feel that I'm visiting a friend's house. The first time I was very nervous. I've been playing in black tie since I was 12, but my hands were shaking so badly I couldn't get my garters on."

The American side of the guest list had the usual representation of corporate, political and labor interests, but in addition there were some new faces.

Falk, of television's Columbo series, looking uncharacteristically elegant and well-groomed in his black tie, said that his series is "very big in Japan-like an epidemic there."

Rep. Pat Schroeder (D-Colo.), dressed in a beiga taffeta gown, said she had left her bunny ears at home again, as she did when she visited the Great Wall of China.

Other guests notable in relation to the field of apparel included designer Gloria Vanderbilt, who was a guest of the evening's entertainer, singer Bobby Short, and Sol Chaikin, president of the International Ladies' Garment Worker's Union. Chaikin denied that he had masterminded a fashion show being held today for Mrs. Ohira. who attended the state dinner dressed in a Japenese kimona. But he said he had advised Mrs. Carter on it. He added, "The textile, apparel and clothing industries employ one out of every eight manufacturing employes in this country."

Film director Francis Coppola, one of the last guests to arrive, carried a large package tied with a pink ribbon, a gift for the prime minister. It was accepted for him by White House security officers. Coppola said that Japan is one of his big interests and that he is currently planning "a really large-scale film that deals with many things, but whose main theme is Japan and America-almost a love story.

"I have always been interested in Japan," he added. "As a kid, I loved 'Madam Butterfly,' and my favorite filmmakers are Japanese." He added that he had been involved in making a film with Akira Kurosawa.

Coppola is well-known for such films as 'The Godfather," and "The Conversation." The film that has been dominating his life for the last four or five years, "Apocalypse Now," is virtually completed, he said, and will be shown at the Cannes Film Festival later this month. He said it has been cut to two hours and 40 minutes and, "It will be worth the wait-it is for me. I know its flaws, but it's on a whole new level."

Maynard Jackson, the mayor of Atlanta, said he would decide later on whether or not to run for the Senate seat now held by embattled Sen. Herman Talmadge. "I will decide by July," he said, adding that the determining factor will be "whether I can win or not."

Richard Drayne legislative consultant, humor writer and former press secretary to Massacnusetts Sen. Edward M. Kennedy-also was a guest. Drayne said he had had a part in writing Rosalynn Carter's speech to the Gridison Club last month said, "She was gracious enough to invite us to the dinner tonight."

Bill Rodgers, winner of this year's Boston Marathon and two previous ones, said that the president had called him up to congratulate him and invite him to last night's dinner the day after he had won the race. His wife said that on the previous day an imposter had identified himself as ABC News and Sports chief Roone Arledge, so that when President Carter called she was skeptical. "I said, 'Oh, sure."

Earlier, Mrs. Ohira and Mrs. Cyrus Vance had attended a luncheon with cabinet, congressional and diplomatic wives, at Woodlawn Plantation, while their husbands conferred in Washington.

There was no overt references to U.S. Japanese trade problems, but in her response to Mrs. Vance's toast, Mrs. Ohira obliquely acknowledged the situation.

"With the kindly cooperation of all of you," she said through an interpreter, "my husband's visit to the United States will, I hope, contribute to the enhancement of friendly relations between the United States and Japan." CAPTION: Picture 1, Clockwise from lower left: Peter Falk, Rosalynn Carter, Prime Minister Ohira and President Carter, by Joe Heiberger; Picture 2, Nancy Fuqua and Peter Falk; by Joe Heiberger-The Washington Post