If my cousin has signed (using a POA) checks belonging to our deceased aunt, what legal action can be taken and is the bank liable?

The bank is not liable, since the POA would seemingly give him authority and the bank is not required to inquire into the facts (e.g. to verify whether your aunt is dead or alive, or the purpose of the checks. That said, what your cousin did is illegal, and the executor or administrator (the representative of the estate) could sue him to recover the money; someone with knowledge of the situation could also report him to the police, and could inform the bank so they do not allow it to happen in the future. A POA expires with the death of the person granting it, so the POA is no longer in effect--after death, only a will (if there is one) directs what happens to the estate, and only the executor (if there is a will) or the court-appointed administrator (if there is no will) can take action on behalf of the estate. (Also, a POA only allows the person to act in the interests of or for the person granting the POA, so taking checks for one's own benefit would be a violation of the fiduciary duty owed by the person granted the authority, also known as the attorney in fact, to the person who gave them that power.)