WDVM-TV management and negotiators for the American Federation of Television and Radio Artists reached agreement on a new contract late yesterday, averting the possibility of a strike at Channel 9. No details of the accord were available last night, but one AFTRA negotiator said, "We've settled and everything's fine." The talks had faced a midnight Friday deadline . . .

Sylvester Stallone was injured while filming fight scenes on the set of "Rocky IV" in Canada and has been hospitalized in Santa Monica, Calif., for treatment of his injuries and the flu, publicist Dick Delson said yesterday. He said the actor probably would be released from the hospital over the weekend . . .

British Ambassador Sir Oliver Wright opens the gardens of the British Embassy to the public today from 11 to 4 for strawberries and cream on the lawn. The fete benefits the Salvation Army's Camp Happyland program, which offers underprivileged children a summer camp in Virginia. The price is $4 a head . . .

"A Soldier's Story" was named the best mystery movie of 1984 and "Briarpatch," by Ross Thomas, the best novel at the annual Edgar Allan Poe Awards ceremonies yesterday. Edgars, given by the Mystery Writers of America, also went to R.D. Rosen for her first novel, "Strike Three, You're Dead," and to Warren Murphy and Molly Cochran for the paperback "Grandmaster," a mystery involving chess . . . -- Desson Howe