Medical term for deafness

The suffix -acusis pertains to hearing, and is normally combined to form words like presbycusis (presby + acusis, age-related hearing loss) and paracusis (para + acusis, any hearing impairment).

When you combine the an- prefix (meaning not or without) with -acusis, you get anacusis -- deafness.

Deafness is the best single word you'll find, I think, though hearing impairment/loss is probably more common in the medical world.

Anacusis (from Gnawme's answer) is a medical term that means complete deafness.
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For your list, there's ageusia, the loss of the sense of taste, which should probably replace aphasia, since speech isn't a traditional human sense.

Following the pattern of anosmia and anopia, the equivalent for hearing would be anauria, from aural. Unfortunately, I can't find any evidence that it's an established word.