oracle 11gr1 to oracle 11gr2 hpux to linux
 

what the easiest way to migrate from hpux oracle 11.1.0.7 to linux oracle 11.2.0.1, datapump/rman ?

The easiest way is to do an upgrade :)

I would *definitely* check if rman is supported for these two versions.

And if it's certified, then yes, my vote would be "rman":

http://www.dba-oracle.com/t_rman_export_expdp.htm