Both examples are grammatical. In ① and ②, both either and too are working as adverbs.
Adverbs (and more generally adverbial phrases) can complement verbs, adjectives or, as in ① and ②, clauses.
I am unable to hear either.
"Either" in the above sentence complements the whole clause "I am unable to hear". It is used to indicate that the clause is adding some information to the preceeding sentence. As noted by the OP, "either" is used for this purpose only when both sentences express negation. In ①, "unable" provides this negative meaning in both sentences.
Other examples of this usage of either (taken from the dictionary linked above):
You don’t like him, do you? I don’t, either.
It won’t do any harm, but won’t really help, either.
I was too tired to go. And I couldn’t have paid my way, either.
If any of the sentences, as in example ②, does not express negation, then the adverb "either" is infelicitous, and "too" should be used instead:
Note that both "either" and "too" link one clause with the preceding sentence, and hence, there must be a reason to link them.
In the case of ①, both sentences follow the same pattern: "I am unable to".
In the case of ②, more context is needed to make this reason patent, e.g.:
Yesterday was a terrible day: I felt humiliated at the party last night. I was unable to sleep well, too.
Out of the three provided, the last one is most correct:
I neither belong to "classA" nor "classB".
"Neither" and "nor" are normally used in the pattern, "neither 'A' nor 'B'". The subject, "I", comes before "neither". I think the most correct way to say this is:
I belong to neither "classA" nor "classB".
Best Answer
I think you can say "Neither is Martha".
In one of the most recent news about Buttigieg replying to Biden, you can read the following (please check the full text here):
I believe that Buttigieg speaks proper English and he uses "neither is he" in his answer.