First check what are values for $APPLTMP and $APPLPTMP set to. Directories pointed out by these values should be there in UTL_FILE_DIR parameter.
If you want to add /u01/temp to UTL_FILE_DIR then add /u01/temp to UTL_FILE_DIR in init.ora..
As you see 3 values of /usr/tmp then remove unwanted /usr/tmp entries from init.ora.
/usr/tmp is 10GB, I think it is sufficient value. You write cronjon to clear contents of it. Timeline based on your requirement.
Is it possible to remove all /usr/tmp in init.ora and replace it with /u01/tmp?
You need to clean old files in temp directory. But ensure do not run into this issue discussed in (Doc ID 760256.1) if few directories (under tmp) time is being cleaned
Hope this helps!
But we will delete only 5 days old files so if .oracle is active its date will be current, right?
if the files are being written to /usr/tmp by oracle application then it must be of value $APPLTMP or $APPLPTMP. I would suggest you to change value of $APPLPTMP and $APPLTMP to /u01/temp (or your value) in XML file and run autoconfig. I would suggest to still keep one value of /usr/tmp in init.ora.
As per as cleaning is concern, 5 days of files is good value.