What is the most appropriate answer (American way)?
Yes, John speaking.
Yes, it is him.
Yes, it is he.
I need to answer calls when interviewers/hiring managers call.
I would avoid “it is him” and “it is he” if you are trying to stick to idiomatic American English. They are not grammatically wrong, but you would not normally hear someone speak of themselves this way on the telephone.
Your other choices are good ones. Another is: “This is John” (or, “Yes, this is John”).
The technically correct answer is "This is he". This is because the verb "to be" is mostly used in a special form called the copula, or less precisely "linking verb." With copulative verbs no action is indicated, rather a state of being is indicated, and so the second substantive, called the predicate, doesn't take the objective case. Which is to say, both take the nominative form, the second being called the nominative predicate.
I think it is a curious rule in English, but it seems to be common in other languages too. However, "this is him" is very common too. Some pedants might bristle at it, and your hiring manager might be one such pedant. On the flip side "this is he" has a slightly hyper correct, pretentious tone to it, and that might tick off your hiring manager too. Of course your hiring manager might be a reasonable person and not care one whit.
I suppose it is easiest to avoid the problem by simply answering, "Yes, this is John."
Yes, it is him/he doesn't sound like a good way of talking about oneself, I'd drop that one immediately.
Yes sounds too short and impolite.
Yes, John speaking and yes, speaking both sound perfectly fine. I'd stick to those!
Since you are looking for an answer to "Is this John?", this implies that you must have initially answered the phone with "Hello". This is indeed the normal default telephone greeting in the US.
I'd suggest that if you're expecting an important call that's directed to you, that you simply answer the phone with "John Smith" or "This is John".
I.e., instead of:
"Is this John?"
"Yes, this is him, er, he, er, I'm John."
You could just have:
"Hello, John, I'd like to offer you a prestigious, highly paid sinecure!"
It's not out of the ordinary at all, in fact it's commonly used in business. It answers the implied question immediately, leaving little room for confusion or awkwardness.
It is would be quite unusual. Rather,
[Yes], this is he.
[Yes], this is John.
[Yes], [John] speaking.
I would use: Yes, this is John speaking.
"Yes," or "Yes, speaking" both do nicely. There might be particular conventions depending on the country you're in, but to my Canadian ear, both sound fine to me.
I would tend to answer "That's me". Probably grammatically completely wrong but idiomatic here in Scotland. The other answer I often hear is "Speaking".