Robert S. Strauss came home from a week-long four-nation tour of the Middle East yesterday with some limited diplomatic successes, signs of progress on oil supplies from Saudi Arabia -- and an idea for a Christmas card for Jimmy Carter.

The Christmas card idea came to Strauss on Friday as he broke away from a partly of perspiring, tired diplomats who had just helped him wrap up his first exercise in negotiating peace between Arabs and Israelis.

Striding over to stand in front of the fluttering Egyptian, Isreaeli and American flags that his Egyptian hosts had raised, Strauss called out, "Would you mind taking a picture of me here?"

Then, turning to his wife, Strauss said elatedly: "helen, this will make a darned good Christmas card to send out all around the world. Maybe the president would like to have some to send out, too."

Turning to a reporter standing near him, Strauss added with a grin: "Well, I'm, not going to stop thinking politically once in a while, even if I am becoming a statesman."

Also stuffed into the Texas politician's new "statesman" briefcase were hints of a still tentative transformation of the U.S. role in the Middle East geared to Strauss' unabased, high velocity entrance onto to the Arab-Israeli stage.

For Strauss, the trip advanced an already beginning metamorphosis from his image as a quick-fix Washington power broker into something approaching the statesman's image that he mentioned only partly in jest.

For the United States, it brings on a new style and new scope to Middle East diplomacy that is as colorful, audacious and openly political as the previous style of Secretary of State Cyrus R. Vance and his aides has been austere, lawyerly and technical. Moreover, the adaptation involves a new emphasis on American business and its ability to export at least one large chunk of its free enterprise values and methods to the Middle East to underpin peace there.

Just before opening a week of separate Meetings with Isreal's Prime Minister Menachem Begin, Egyptian President Anwar Sadat, Jordan's King

Hussein and Saudi Arabian Crown Prince Fahd, Strauss acknowledge to reporters that perhaps the most immediate task he faced was to establish credibility and to dispel "concern that I'm out here to play games, to stall until we get past the [1980] elections."

Acknowledging that he and Fahd had voiced sharp differences over the Egyptian Israeli peace treaty, Strauss said they had spent two-thirds of their time discussing "bilateral issues on which we have strong agreement." He refused to list them before reporting to Carter, but other sources indicated they include a formal Saudi assurance that a rumored temporary production increase of up to 1 million barrles a day of crude oil is on the way.

Strauss clearly did not succeed in dispelling all of the doubts in the region about his slickness and his willingness to stay the course in what Strauss himself called "a long, difficult and tedious process,"

He did not even approach the explosive Palestinian issue that is at the heart of the new round of negotiations sponsored by Carter, except in an elliptical and ultimately masleading way at press conferences that kept alive fears that he is playing games. He confused reporters by saying he had met with "Palestinians" and then refusing to explain that he has met with Palestinian-born U.S. citizens.

But at each stop on the trip Strauss grew visibly more relaxed and confident as he received the feedback on what he does best, which it to talk positively about himself, about Carter, and about each of the leaders he saw and whom he hopes to sell to each other when the time comes to close a deal.

Prince Fahd, long umoured to be ill, "was strong and vigorous, as strong as horseradish," Strauss said. Dressed in an elegantly tailored outfit on his way to see Hussein, Strauss paused to tell reporters, "I'm whereing my king suit today, fellers."

Sadat "is a big picture man, a strategic thinker. He spent 20 percnt of the time we talked explaining Begin's difficulties to me and how Begin continues to grow. Sadat says Begin is 'a change-ed man' since the treaty was signed." Begin in turn spent his time boosting Sadat to Strauss, and all three praised Carter.

Outlines of a fresh Strauss strategy did emerge from his encounters and from the three-nation negotiating session in Alexandria that moved the Wast Bank autonomy talks beyond an impasses on a formal agenda into committees that will handle much of the detailed haggling.

That strategy evidently will resmble the approach Strauss used in assembling the complex international trade bill that the administration hopes to move through the Senate with Strauss' help this week.

A steady stream of messages and telephone calls to Carter and congressmen Last week mirrored the caution Strauss used in securing his political flanks at home before moveing to identify the tradeoffs in imports and exports that would interest other nations in dealing with him.

"I'm a closer," Strauss said today in an almost explicit contrast of his approach to the State Department. "I want to close deals and seal them off so we can move on. Most public servants aren't closers. People will sit around and talk and debate and lose deals if you let them."

His early strategy is apparently to try to reassure both sides that they "can both come out of this winners" if they will invest their trust in tim. Invited repeatedly to echo the State Department's condemnations of Israeli settlements on the west Bank as "illegal," Strauss took another approach.

"The settlements have provent to be an obstacle to progress toward peace," he said, "and an obstacle to Israel's stating its case before world opinion. Even if they do lend themselves toward Israeli security objectives, it has to be asked if that is sufficient compensation for what Israel loses on the peace process and in world opinion. My answer is no. It is not worth it."

Strauss made that statement to reporters a day after the Israelis had flow him around the West Bank by helicopter to demonstrate how exposed Israeli cities would be to Arab attack if the 55 settlements on the West Bank were not maintained. As this argument was being made to him on one stop of the tour, Strauss answered softly: "Governments change, and circumstances change."

Strauss' soft approach and his ast record as a fund raiser for Israel did not dispel Israeli fears of eventual U.S. pressure for concessions in the West Bank autonomy negotiations. The Israeli delegation at Alexandria raised objection to full and formal U.S. participation in the communique that set up the negotiating committees, but Strauss wore them down on the point with his repeated insistence that the deal be closed now, under his seal.

Before arriving in the Middle East, Strauss said publicly that he was ready "to take scars" and generate "a bit of a flap" if he needed to do so to get things moving. In fact, he played his hand cautiously, reminding friends privately that "I talk lose but I play tight."

Pressed at a Israeli press conference to discuss his views on Palestinian legitimate rights and self-determination, Strauss phrased his answer in a way more likely to disarmed the press: "Out in West Texas they taught me not to stick my foot in it without knowing what 'it' was. So I think I won't answer that question if you don't mind."

Strauss spent much of his first tour listening. He let Prince Fahd structure their conversation into two separate parts on the peace moves and then on "other issues," which Strauss said included oil.

"The prince did not made any linkage whatsoever," Strauss said afterward. "It was like two separate conversations in different languages."

"I got into that conversation very gingerly," Strauss said of his meeting with Fahd, the day-to-day head of government of the world's largest petroleum-exporting country."If it had gone badly I would have never recovered from that in this job." CAPTION: Picture, ROBERT STRAUSS . . . cites limited success