Now that "Social Security" has closed at the National Theatre, director Mike Nichols and actress Marlo Thomas have moved the show on to the Barrymore Theatre in New York, where three weeks of previews begin tonight in preparation for the Broadway opening. Now that one cast has moved from the Wyndham Bristol Hotel, the cast of the new National play, "Long Day's Journey Into Night," has moved into the hotel, including Jack Lemmon and his wife Felicia Farr, who dine often in the Bristol Grill . . .

Moving onward: Walter Wurfel, former deputy press secretary to President Carter, is leaving the public relations firm of Ruder, Finn & Rotman to become vice president for public affairs and communications at the National Association of Broadcasters. Now that should fill up the white space on his business card . . .

After covering every president since Harry Truman, Ralph Harris, the White House Reuters correspondent, was mildly roasted yesterday on his last day of work at the executive mansion just before press spokesman Larry Speakes' morning briefing. A number of White House correspondents thought for a moment that a long-desired coup had taken place when Speakes took a seat off to the side and Jerry O'Leary, Washington Times White House correspondent, took over the lectern. O'Leary remarked how the 65-year-old Harris had picked up "our language almost immediately" on coming to Washington from England after World War II. After Speakes was able to get back the microphone, he said he was relieved to see that Harris was one person not leaving the White House to go to work for Bob Gray or Mike Deaver . . .

Katerina Lycheva, the 11-year-old Soviet girl on a peace mission, arrives in town this morning and is in for a surprise when she checks in at the Hyatt Regency on Capitol Hill. In her suite with an appropriate view of the Capitol will be an 11-foot chocolate rabbit created by the hotel's chef Jim Bellows, who will also present the young diplomat with an Easter basket. Last night in New York Lycheva went for a bit of East-meets-West Americana by attending "Big River," the Broadway musical based on "Huckleberry Finn." The show is scheduled to come to the Kennedy Center next month . . .

It's now official. Prince Andrew will marry Sarah Ferguson in Westminster Abbey July 23 for a wedding at the height of the tourist season. All those Washingtonians who just know the invitation is in the mail can now make flight and hotel reservations. That is, of course, those who would rather stay in the city than in one of the "treasure houses" . . .