Crontabs can live in different places on different systems, but generally when you run crontab -e you're editing the crontab of the current user, which is generally placed in /var/spool/cron/{username}. If you do sudo crontab -e that edits the crontab/file for root. There can be other files nested in /etc/cron.d, /etc/cron.hourly, /etc/cron.daily et cetera as well.
To find out where those old cronjobs are still defined, you can recursive grep the name of that unique log file you mentioned (if the log file is part of the command in the crontab). grep -r "{unique log file name}" /etc and /var/spool should find it. If the log file name isn't in the command, grep for some other unique string from that cronjob that would stand out amidst everything else in /etc.
To add timestamps to log output, you can pipe it through ts.