Find big files and remove them if possible:

find / -mount -size +8096 -lsfind / -mount -name core -lsdu -sh /* (and repeat for subsequent dirs on /)

Probably something is flooding your / or you have to many old kernels. Cleaning up will help, your / should be big enough because you've a seperated /var and /usr (and /data ...).

references http://serverfault.com/questions/164413/100-disk-full-on-centos