The correct choice is C. A simple rule of thumb is that 'who' serves as the subject of a verb while 'whom' serves as the object. In the pertinent clause, "...his parents, both of ____ were hearing-impaired,..." the inserted pronoun must serve as the subject of the verb "were." Hence, 'who' is the correct option. You can see it better if you replaced "his parents" with (say) "his father." So, the sentence becomes "...his father, ____ was hearing-impaired,..." Clearly, you would use the pronoun 'who' in this case.
Going by the same reasoning, in the sentence "I can invite ____ I wish," the correct answer would be "whomever" since it serves as the object of the verb "invite."