"Stray Dogs," a new play by Julie Jensen, is the winner of the Foundation of The Dramatists Guild/CBS New Plays Program at Arena Stage. Jensen will receive a $5,000 award and a full production of her play in the Old Vat Room in June.

Jensen's play was chosen from 1,257 scripts received by Arena between July 1 and Sept. 15. Only unproduced, full-length plays written by American playwrights were eligible for the competition.

Set in rural Utah during the 1950s, "Stray Dogs," which will also be given a rehearsed reading in the Kreeger Feb. 9, is a tale of family strife, focusing on a young woman's efforts to raise her two boys while married to a rowdy alcoholic.

Receiving honorable mentions in the contest were "The Emigration of Adam Czernak," by Theodore Herstand, and "The Poets' Corner," by Harry Kondoleon. The two playwrights will each be awarded $1,000 and Herstand's play will be given a reading in the Kreeger March 16.

Other theaters selected for this year's FDG/CBS New Plays Program, now in its fourth and final year, are the Los Angeles Theatre Center; the Crossroads Theatre Company in New Brunswick, N.J.; the Hartford Stage Company in Hartford, Conn.; and the Northlight Theatre in Evanston, Ill. Each winning production will be viewed by a panel of American playwrights for a final National Award of $10,000 to be shared by the playwright and the theater. 'Mise'rables' Here in December

"Les Mise'rables," the hit musical currently playing at London's West End, is scheduled to come to the Kennedy Center in December before moving on to Broadway in March 1987. It is not yet known how many members of the Royal Shakespeare Company will recreate their roles here. Based on Victor Hugo's classic novel, "Les Mise'rables" follows Jean Valjean, a victim of society, through three decades of early 19th-century French history. Presenters of the musical are still to be named. Can't Beat the Price

Sure, it's held in an auditorium and not a theater; and sometimes the performers are without costumes and props. But the Source Theatre's "Saturday Theater" series -- five plays performed at the D.C. Public Library -- is free. And in this day of $40 theater tickets, that ain't too shabby.

"Theater is just beyond the economic reach of an awful lot of people," said Octave Stevenson, chief of the language and literature division of the D.C. Public Library. "This is an opportunity for a lot of people to see some good theater."

The series, which the Source does as a community service, includes: "Educating Rita," Feb. 1; "The Country Wife," March 8; "Macbeth," March 22; "The Informer," May 10; and "A Soldier's Play," June 21. All performances are at 1:30 p.m. in Room A-5 of the Martin Luther King Memorial Library; free parking is available. Reservations are not necessary but it is recommended that you call 727-1281 before each show for any program changes. Televising Brecht and Weill

Arena Stage's 1984 production of Brecht and Weill's musical "Happy End" will be televised at 10 p.m. Saturday on WETA Channel 26 with stereo simulcast by WETA-FM (90.9). The show, taped in June 1984 by Boston's WGBH, is part of the national broadcast of PBS' "America's Musical Theater" series. The musical melodrama about Sister Lillian Holiday, a Salvation Army lieutenant who trys to save the souls of Chicago gangsters, features a cast of 24, including Richard Bauer, Casey Biggs and Marilyn Caskey. Odds and Ends

The AT&T Foundation awarded Arena Stage $10,000 to support the residency of Sharon Ott, who will direct the production of Edward Bond's "Restoration" Jan. 17 through Feb. 23 . . . "Free Fall," a new play about alcoholism by David Price-Gresty, will receive a staged reading Jan. 27 at d.c. space. Free; call 393-0255 or 347-4960 for more information . . . Northern Virginia Theatre Alliance's fifth annual one-act play festival continues this weekend at the Reston Community Center; call 476-1111 . . . Horizons Theatre will stage a special half-price performance of "Automatic Pilot" for working members of the theater community Monday; $6 tickets can be reserved by calling 342-7706 . . . Visions Inc., a new theater company, will present its inaugural production -- "Strange Snow," a drama about two Vietnam veterans -- tomorrow in the new theater of the Duke Ellington School for the Arts. For tickets to the show, which runs through Feb. 8, call 966-4691.