Ansible: have sudo but no root

Well, you simply cannot execute /bin/sh or /bin/bash as your /etc/sudoers shows. What you could do is change ansible's default shell to something else (variable executable in ansible.conf).

Since your sudo policy allows everything by default (does not seem like really secure to me), and I suppose ansible expects an sh-compatible shell, as a really dirty hack you could copy /bin/bash to some other path/name and set the executable variable accordingly (not tested).