The symptoms described are similar to that of Bell's palsy, suggesting the involvement of multiple cranial nerves. The cranial nerves affected in this case are:
1. Symptom: move the muscles on the right side of the face
Cranial Nerve/s affected: VII (Facial Nerve)
2. Symptom: loss of taste
Cranial Nerve/s affected: VII (Facial nerve), IX (Glossopharyngeal nerve), and X (Vagus nerve)
3. Symptom: dry mouth
Cranial Nerve/s affected: VII (Facial nerve) and IX (Glossopharyngeal nerve)
4. Symptom: inability to close the right eye
Cranial Nerve/s affected: III (Oculomotor nerve)