The A-H and Topps (makers of Bazooka bubblegum) both point to a musical instrument (a slide kazoo) created in the thirties by Bob Burns (a comedian) called a bazooka as the origin of the name of the bubblegum and the WW2 anti-tank weapon. Furthermore, Topps says that Bazooka Joe, the comic, was first created in 1953. The jeep (general purpose vehicle) on the other hand did get its name from the Popeye comicstrip.

http://www.topps.com/Confectionery/conf_history.html
http://www.bartleby.com/61/53/B0125300.html
http://www.geocities.com/captainkazoo/burns.html