Well, I think its one (or more) log files which have grown too large and need to be removed/backedup. I would suggest going after the big files first. So find all files greater than 10 MB (10 MB is a big enough file size, you can choose +1M for 1MB similarly)
sudo find / -type f -size +10M -exec ls -lh {} \;
and now you can identify which ones are causing the trouble and deal with them accordingly.
As for your original du -a / | sort -n -r | head -n 10 command, that won't work since it is sorting by size, and so, all ancestor directories of a large file will go up the pyramid, while the individual file will most probably be missed.
Note: It should be pretty simple to notice the occurence of similar other log files/binaries in the location of the files you so find, so as a suggestion, do cd in to the directory containing the original file to cleanup more files of the same kind. You can also iterate with the command for files with sizes greater than 1MB next, and so on.