Are there any relationships between unilateral deafness (because of mumps) and meniere?

Possible: Perhaps. Mumps causing a severe sensorineural hearing loss in childhood, may not affect the vestibular system until years later, perhaps due to delayed endolymphatic hydrops. While viruses are felt to be important etiologic agents, evidence is mostly circumstantial. At the present time only cytomegalovirus and the mumps virus have been cultured from the perilymph of affected ears. See Otologist.