What cranial nerves are involved in proprioception?

Optic nerve (II) the ocular motor nerve (III) moves the eyes. Other cranial nerves are: Trochlear nerve (IV) and Abducens nerve (VI) which contribute to rolling the eyes.

hypoglossal

Optic nerve CNII

Vestibulocochlear nerve (CN VIII). More specifically vestibular nerve of CN VIII is responsible for equilibrium and balance.

Vestibulocochlear Nerve (VIII)