Tomcat is a web application server. The easiest way to find out if it is running is to do a
ps -ef | grep -i catalina command. This will show up any process with catalina(tomcat) in it. If you see a line returned other than a result with "grep -i catalina" in it, it is running.
If you are root, you should be able to stop the service by either running
/etc/init.d/tomcat stop or
/etc/init.d/tomcat as stated in @Eric DANNIELOU comment. Another method is to goto the catalina home area, shown in the line returned by the prior
ps -ef | grep -i catalina command. It is the directory after "-Dcatalina.home=". Navigate to that directory and then into the bin directory inside of it. You should see a catalina.sh file in there. Run
./catalina.sh stop and that will stop tomcat.
As for if it is set to startup, most distros(I believe all but not sure) have /etc/rcX.d directories, where X is the run level. If this is a server it is likely booting into run level 3. Go into /etc/rc3.d and see if there is a SXXtomcat or SXXtomcat6 file, where XX is a number. If it exists there, you should be able to delete that file to prevent it from starting up. If this is a RedHat server it may be easier to use chkconfig command. You can do a
chkconfig --list | grep tomcat and it will lists the run level and on or off for that run level. Look at chkconfig @ linuxcommand.org for more help how to disable a service.