How do I deal with 'sudoers.so must be only be writable by owner'?

22h has it right, but because of the sudoers.so issue, you won't be able to run sudo to fix the permissions.

So you are going to have to drop to a root shell as described here: How do I boot into a root shell?

(Essentially rebooting, holding the left Shift key for Grub to come up, "Advanced Options" "recovery mode" "network" and "root").

Then you will need to:

chown root:root /usr/lib/sudo/sudoers.so
chmod 644 /usr/lib/sudo/sudoers.so

Which should solve this issue.

Try this,

ls -l /usr/lib/sudo/sudoers.so

If the first word of the output is something other than

-rwxr-xr-x

we have to remove the write permissions from group and others.

pkexec chmod go-w /usr/lib/sudo/sudoers.so