Easy with the right tools.......
My tiny little wife removed 30 yards of vinyl and luan underlayment by herself in about half of a day this summer in preparation for re-doing our floors.
Tools:
Floor scraper from Harbor Freight - sort of looks like a sidewalk ice scraper, but with a 15-degree kink in the head for leverage
Imitation "Wonder Bar", also from Harbor Freight - a flat wrecking bar
Stanley knife with sharp blades
Use the Stanley knife to score the vinyl and luan underlayment in 3ft x 3ft sections or so, then use either of the other tools (you need more room for the handle of the floor scraper) to pry up the floor sections. You will find thousands of staples but most willl come loose with the luan.
Obviously a hammer helps too.