How can I free space in oracle mount point (/u01/app/oracle/)? My question is what can I delete or how can I free space so that I can log onto oracle via sqlplus as sysdba. When I execute the command df -k to see the free space in the current directory it appears to be full and on the other machine its at 52%.

Filesystem                   1K-blocks     Used        Available  Use%    Mounted on

/dev/mapper/rootvq-rootlv    51606140    48985496      0          100%    /
If your oracle installation is on your root volume you should have a look at the DIAG_DESTINATION, e.g. /u01/app/oracle/diag/. If there's a lot of old trace files in there you can safely remove them with adrci. If your oracle installation is on a separate disk you have to check where the space is consumed (/var?) and free space there.