I have noticed that "logs" and "tmp" content take 36GB and 21GB respectively. I need to free up some disk space and currently wondering is it vise to clean them.
Delete logs older than 7 days.
You probably want to add this as a cronjob too.
Before deleting temp-files, you should make sure that nothing is holding them open.
You should set up tomcat in logrotate properly. Something like this as /etc/logrotate.d/tomcat:
tmp you might want to sweep using the find command that pkhamre showed, but I would use logrotate on the log files. You didn't say which distro you're using, but RHEL/CentOS has tmpwatch, which will remove files that haven't been accessed for a defined period of time.