Varsity-you represent Duke at the national level against other D1 programs i.e. scholarship athletes at Duke
Club-you represent Duke at the national level against club competition from other schools i.e. students who were fantastic at the sport and excelled in the varsity squad at their high school and in their hometown/city/region but not quite nationally recognized
IM-you form a group with friends for intercollegiate competition between different groups at Duke including fraternities/sororities, selective living groups, arts/performance groups, etc. etc., meant for the typical student-athlete and is pretty laid-back
Hope that clears things up!