As the error message says: your /etc/sudoers file has the wrong permissions.
the normal permissions (on OS X 10.10) are:
$ ls -l /etc/sudoers
-r--r----- 1 root wheel 1293 Sep 19 2012 /etc/sudoers
so get a root shell in some other manner and issue chmod 660 /etc/sudoers
and/or the appropriate chgrp and chown commands.
To get a root shell, it all depends on what you have left as assets. The failsafe method would be from a recovery partition, but booting in single user mode should be enough in most cases.
Single user mode: boot holding "Command-S" ref: https://support.apple.com/en-us/HT201573