@djones, there have been a few different NRBQ lineups. The one on the 1st album (on Columbia Records, where they back the great Carl Perkins) reminds me somewhat of the first version of Springsteen's E Street Band---a little weak (though not as bad. Springsteen's first drummer was terrible). The eclectic vision is there, but it's not quite realized.
Pianist/leader Terry Adams and bassist Joey Spampinato then enlisted drummer Tom Ardolino and guitarist/singer Al Anderson for the band's classic, decades-long lineup. They made a lot of albums on Rounder Records, and established themselves as one of America's great Rock 'n' Roll bands. Fans of theirs include Elvis Costello, Bonnie Raitt, Nick Lowe, Dave Edmunds, and every good musician I know.
Their influences include Rock 'n' Roll, Rockabilly, Jazz (Sun Ra in particular), Blues, Hillbilly, Show tunes, Pop---just about all strains of American music. There live shows were wild, unbelievable explosions of kinetic energy, amongst the best I've ever witnessed. And I saw The Who with Keith Moon twice!
