Go go to moodledata folder /temp/backup/
Contained there in one might find .log files of more then 0 byte size that could give you clues. .log files are text and one can open them with a text editor.
You also might find folders with long hashcontent names (a bunch of letters and numbers). Contained there in one might find either in-complete backups (possibly all 20 of those 'unfinished' referenced in the message). If you inspect the moodle_backup.xml file one can determine the course itself. If you see .mbz files contained therein, it could mean the backup for that course did complete, but the 'copy' routine to move the course backups to other destinations (filedir/automated backups with an alternative directory) failed. One can physically move those .mbz's, however.
mv *.mbz /home/backups/
Strongly suggest going to courses found by inspecting moodle_backup.xml files and running a backups manually for those courses to see what transpires.
Once you've explored all that you can of moodledata/temp/backup/ (and moved any .mbz's found to another location), it is safe to remove any/all files/folders from /moodledata/temp/backup/. Leave the 'backup' directory, however. That should free up some room on a very limited drive.
Strongly suggest moving the server to a system that has more space allocated. Even if one solves the current issue, it's very possible one will face it again. Moodle courses seldom shrink in size ... most often, they grow - thus requiring more space. Teachers might keep copies of previous courses hidden and un-used while using a re-set course. In other words, the number of courses are also likely to increase.
'spirit of sharing', Ken