Answer by taking a quote from the following article:

Late Night with Conan O'Brien is an American late-night talk show hosted by Conan O'Brien that aired 2,725 episodes on NBC between 1993 and 2009. The show featured varied comedic material, celebrity interviews, and musical and comedy performances. Late Night aired weeknights at 12:37 am Eastern/11:37 pm Central and 12:37 am Mountain in the United States.

The show's house band was The Max Weinberg 7, led by drummer Max Weinberg, who also served as a sounding board for O'Brien on the show (more so after Andy Richter's departure). The other six members were Mark Pender on trumpet, Richie "LaBamba" Rosenberg on trombone, Mike Merritt on bass, Jerry Vivino on saxophone and brother Jimmy Vivino on guitar, and Scott Healy on keyboards. James Wormworth served as backup drummer when Weinberg went on tour with Bruce Springsteen. With the departure of Andy Richter, Max Weinberg assumed a bigger role as an interlocutor for O'Brien's jokes. One common running gag was Max's awkwardness on camera and his apparent lack of chemistry with Conan. Weinberg was often used in sketches as well, which usually revolved around his purported sexual deviance (mostly a penchant for bedding barely legal groupies), although long-running sketches also spoofed Max's lack of knowledge of current affairs.  "LaBamba" was also used as the butt of many of Conan's jokes. These humorous sketches usually revolved around LaBamba's sizeable mustache, his poor acting skills, and his alleged inability to read written music. Mark Pender would often sing songs on the topic of a current event which ended with him screeching uncontrollably and climbing the risers into the audience. All members of the 7 had successful side careers as studio musicians.  As is common in the talk show format, the Max Weinberg 7 performed the show's opening and closing themes, played bumpers into and out of commercial breaks (they actually played through the entire break for the studio audience), and a short piece during O'Brien's crossover to his desk after his monologue (except for several months beginning in April 2008, where a commercial break was inserted at that point). The show's opening theme was written by Howard Shore and John Lurie (a finalist for the job as band leader). The show's closing theme was called "Cornell Knowledge", and was lifted from Jerry and Jimmy Vivino's first album together. However, on Late Night, it was played at a much quicker tempo than the album version.  The band played a wide variety of songs as bumpers--usually popular music from a variety of eras. Weinberg sometimes took extended leaves of absence to tour with Bruce Springsteen as the drummer for his E Street Band. During his absence, temporary replacement drummers were hired (most commonly James Wormworth), and the band was led by Jimmy Vivino ("Jimmy Vivino and the Max Weinberg 7").

What style music did they play?
The band played a wide variety of songs as bumpers--usually popular music from a variety of eras.