"sudo su -" utterly undermines the security of sudo and su. You're using sudo to become root to then run su to become a third user? wtf? I know it's a very common thing to do, but it's insane.
"sudo -i -u sysadm" will achieve the same thing properly. sudo will simulate an initial login for the given user and be aware of it.
And for the password part, I believe you can have a sudoers entry of:
test-user ALL=(sysadm) NOPASSWD: /bin/bash