ROCK: ELVIS COSTELLO, TWICE

ELVIS COSTELLO knows how to turn concert appearances into events. In 1979, he played three New York clubs in one day. And his current, sold-out engagement, ''Costello Sings Again,'' calls for five nights at the Broadway Theater, 1681 Broadway at 53d Street, with five different programs - three with his longtime British band, the Attractions, and two with an American band, the Confederates, plus guests and gimmicks.

Opening night, Tuesday, featured Mr. Costello in his most familiar guise, leading the Attractions in a breakneck, virtually nonstop two-hour set including many of his best-known songs. Wednesday, when he played solo and with the Confederates, he was a changed performer -talkative, droll, almost casual.

Mr. Costello's songs revolve around carefully crafted, sharp-edged lyrics, ranging from free-associative conundrums to blunt statements - most often about betrayed, angry lovers. He delivers those words with fierce emotion, savoring their anger or sarcasm, stretching syllables and shifting phrases to make them new. While Mr. Costello's husky baritone is not rock's most flexible voice, it suits his sullen, pugnacious, heartfelt verses.

By purely musical standards, Tuesday's was the better concert. The Attractions treat Mr. Costello's songs with rough affection, maintaining an improvisational spirit as they dip into punk-rock, Tex-Mex, folk-rock, lounge-rock, and stripped-down Memphis soul.

Even on Tuesday, Mr. Costello softened the angry-young-man stance he assumed in the late 1970's; between accusatory songs, he smiled. He also dropped a quote from ''Lullaby of Broadway'' into ''Watching the Detectives'' and added a verse of ''On Broadway'' to ''Clubland.'' All that kept Tuesday's show from being one of the year's finest rock concerts was a brutal volume level that turned well-made songs into bludgeons.

On Wednesday, Mr. Costello appeared with an acoustic guitar and a home-movie-size screen that showed modern-art slides; his comic timing was easy. Between solo versions of his songs (as well as the Hollies' ''King Midas in Reverse'' and the Psychedelic Furs' ''Pretty in Pink''), full of dynamic ups and downs, he even explained some of his own arcane references. Next, he was joined by T-Bone Burnett for a few countryish, close-harmony duets - they introduced themselves as the Coward Brothers - followed by a cheerful audience sing-along on ''Twist and Shout.''

Finally, the Confederates - featuring the twangy lead-guitar lines of James Burton, a longtime member of Elvis Presley's band - shifted the music into country and rockabilly territory, putting a loose-limbed back beat under Mr. Costello's words. The playing was spontaneous rather than precise, but Mr. Costello came close to being lovable.