[Thu Aug 25 08:23:39 2011] [error] [client 18.104.22.168] PHP Warning: Unknown: open(/var/lib/php/session/sess_7eq8blaus5bfv85f4cqm1o9nn5, O_RDWR) failed: Permission denied (13) in Unknown on line 0, referer: http://clicks.thespecialsearch.com/x...ahRsEnoabBj4k=
[Thu Aug 25 08:23:39 2011] [error] [client 22.214.171.124] PHP Warning: Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/var/lib/php/session) in Unknown on line 0, referer: http://clicks.thespecialsearch.com/x...ahRsEnoabBj4k=
This lines are showing that your php site is trying to access in /var/lib/php/session.
Maybe you have a function ini_set changing the path, or it is being readed from a mysql database, or from a script outside of home directory of the user.
Did you search for sess_* files? did it find any to see where are being them saved? do you have only one site running on your host?
edit: you could try to find "session.save_path" this in your scripts, if your php code is changing it in real time, it could be done with ini_set... just replace the string in the previous command to search inside files.