British Prime Minister James Callaghan and Vice President Walter Mondale's spontaneous sing-along of Yorkshire drinking songs a few weeks ago at 10 Downing St. may be a hard act to follow at 1600 Pennsylvania Ave. But when state visitor Callaghan turns up there tonight, his musical preferences and Welsh background will have preceed him and almost certainly been provided for.

The Carter White House aide whose job it is to see to such things - and a great deal more - is Social Secretary Gretchen Poston, 45, "born Demcrat" from Kansas City, Mo., who is finding the task absorbing enough that she virtually forgot her own birthday last month.

Her strategy is to try to fit the entertainment at state dinners to the tastes of the guests of honor - and often-expressed but not always successful aim of past Presidents and First Ladies, and part of the Carter's style that began with their first such dinner of Mexican President Lopez Portillo.

"We knew Mrs. Portillo played the piano so that was relatively simple if you could find someone like Rudolf Serkin who was free," says Poston. Serkin was and not only agreed to perform but brought along his piano at his own expense.

Now, less than three weeks and a teapotful of tempests later - Amy Carter's reading habits, Margaret Trudeau's fashion statements and Ohio Gov. James Rhodes' grandchildren, to name three - Poston has settled comfortably into a position one of her predecessors has called "a total commitment, not just a job."

If Poston is inscrutable and uncommunicative about what she thinks of such matters, it is her nature, say friends who portray her as a woman of absolute calm and impenetrable discretion.

"She is the most unflappable person I've ever met," says longtime friend and fellow-Missourian Barbara Eagleton, wife of the Missouri senator, categorically.

Poston seems to have found her niche. "I feel she was cut out for the job," says Mary Hoyt, Rosalynn Carter's press secretary.

"She's a catalyst whose real forte is creativity and imagination," says former business associate Barbara Boggs, who was Poston and Ellen Proxmire that eventually became Washington founded the wedding consulting firm Whirl-Around.

After a half-dozen years in wedding and convention planning, Poston's modus operandi is "working a lot of paper, first. I'm a detail person who feels you have to see it all written out to know whether it's going to work."

She had different plans when she stopped off in Washington in 1960 en route to Japan and a Department of the Army teaching job. A graduate of St. Mary's College in Leavenworth, Kan., she taught school in Kansas City, Mo., public schools for a few years, before taking off to see the world. She got as far as France for a year and Germany for another before heading in the other direction, via a training course at Catholic University here.

When that ended, she had three weeks to kill and applied for a secretarial job in Raymond Poston's law firm. "I'd always passed out ballots and worked in precints."

She joined the Women's National Democratic Club, (and is still a member of its board) and before long was up to her neck politically in fund-raisers. Never interested in seeking public office herself, and married to a man who almost indifferent to politics, Gretchen Poston was a natural for a town like Washington.

The great-granddaughter of a Pennsylvania state senator who had followed Horace Greeley's advice and gone west to Missouri (he eventually started a newspaper that became the Kansas City Star), Poston was loyal to her avocation of politics, but no more so than to her friends.

"She loves to celebrate St. Patrick's Day with little gifts for all of us," says Barbara Eagleton. "And she has lots of Jewish and Irish friends.So last year she gave us all green bagles. She never left a note but you always know it's from Gretchen."

Poston says her friendships may be the outgrowth of a life among women. Fatherless at age 2 and the youngest of three sisters, she went off to boarding school. "It makes you very true to yourself - you learn to give and take easily."

Her friends, indeed, seem legion. There is a long-standing tennis game with Joan Mondale, Nancy Stevenson, wife of Illinois Sen. Adlai Stevenson, and Marge Elfin, whose husband is the newsweek bureau chief here. The game has suffered neglect since Poston went to the White House (and perhaps since Mondale went to Admiral House). She vows, though, not for long.

A "mourning person" who cooks breakfast for her children, Katharene, 4, Ramsey, 10, Carol, 13, and Jeffrey 15, she subscribes to the Carter White House work ethic by instinct, not direction.

In her office by 9 a.m., she may not return home until midnight, should she have to do her other "hat," that of White House talent scout, in the evening. She lives in "the world of the shuttle," flying to New York to catch a rehearsal ("Annie," the musical comedy, a case in point to report back to Rosalynn Carter its suitability as White House entertainment.

Poston's account of how she got where she is today is terse and to the point. Mary Hoyt called her on New Year's Eve to ask if she would like to meet to talk about being social secretary at the White House. Though caught completely by surprise, Poston remembers that "I said 'yes, I would' and hung up."

She met Rosalynn Carter for the first time a few days later and now - in less than three months - sees herself almost as "an extension of Mrs. Carter. If you can't have that feeling about somebody, you can't do it."

She has feelings of "affection, protection and respect" for Mrs. Carter, woman she describes as "a very gracious, classic lady" whose tendency, like her husband's, to less structured procedures in no way connotes an absence of social graces.

"I think the word informal is not right," says Poston. "What I call "informality" is when Mrs. Carter or the President might turn around to talk to somebody."

The Carters strive to make their guests comfortable, she says, but there is also a practical purpose behind some arrangements now beginning to emerge. President Carter likes to be at the same dinner table with Mrs. Carter, Poston says, but he also wants to be with the visiting president or prime minister. Under previous administrations, the President and First Lady presided over neighboring tables. The Carters, however, have been sitting together with each visiting state couple, a "marvelous opportunity to continue the conversation of the visit," says Poston.

Another departure from recent White House practices is the absence of dancing. "The Carters do not object, but it seemed to be an extension to the evening that really doesn't fit."

And if some guests at the three previous White House dinners have seemed reluctant to go home, well, that to Poston is a very good sign.

"Have you ever been to a party that ended on a high note? Well, it's great if you feel that you could have stayed an extra hour."

That, says Poston, is a sure-fire sign to her that a good time was had by all.