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Suppose I am on the phone with someone.

George: Hello. Who's calling?
Myself: Me, Jane. (= It's me, Jane.)
Myself: I (= It's I, Jane.)

Are two of my replies natural and do they mean as I wrote above?
Can my reply with 'I' be also short for the following?

I (am calling.)
I (, Jane, is calling)
I (, Jane, am calling)

I (, Jane, who is calling)

By the way, in sentences like the following, which is grammatically correct?

I, Jane, am calling.
I, Jane, is calling.

Thank you in advance for your assistance.
Comments  
Hi,

I am on the phone with someone.

George: Hello. Who's calling?

Myself: Me, Jane. (= It's me, Jane.)

Myself: I (= It's I, Jane.)

People almost always use 'me' rather than 'I'..

But by far the most common thing is just 'It's Jane'.

Are two of my replies natural and do they mean as I wrote above?

Can my reply with 'I' be also short for the following?

I (am calling.)

I (, Jane, is calling)

I (, Jane, am calling)

I (, Jane, who is calling)

You mean you just want to answer 'I' ? That doesn't give the other person much information. It sounds like you want to be funny, or cheeky.

By the way, in sentences like the following, which is grammatically correct?

I, Jane, am calling. Only this. But it's not a natural thing to say. Too formal.

I, Jane, is calling.

Clive
You'll often encounter conflict of opinion about whether 'I' or 'me' is correct but, whilst it's true that traditional grammars say that only the nominative 'I' is correct, just about everyone says 'me'. The source of the conflict is a mistaken belief that there's a rule of English grammar requiring a nominative form where a pronoun is 'complement' of the verb 'be'. The fact is that though 'I' is not wrong, it's very formal, and accusative 'me' is the normal Standard English way to confirm your identity to someone who knows you but can't see you.

BillJ
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Thank you, Clive, for explaining all my questions.
CliveYou mean you just want to answer 'I' ? That doesn't give the other person much information. It sounds like you want to be funny, or cheeky.
I should avoid saying this then. Emotion: smile

What about replying with "I am" to "Who's calling?"? Is this correct? Perhaps if the person on the other line is someone closed to me or familiar with my voice, I may not need to say my name.
Thank you, too, BillJ. That was very informative and interesting.
BillJThe fact is that though 'I' is not wrong, it's very formal, and accusative 'me' is the normal Standard English way to confirm your identity to someone who knows you but can't see you.
I see replying with 'I' alone in the example is not wrong, but it's too formal that the person saying this might sound funny or cheeky as Clive commented.
Hi,

What about replying with "I am" to "Who's calling, please?" Is this correct? Perhaps if the person on the other line is someone closed to me or familiar with my voice, I may not need to say my name.

I prefer it if people just tell me their name. Sometimes voices sound different on the phone.

I have a friend who never identifies herself on the phone. It's quite irritating.

Clive
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If the person was able to recognize your voice, he or she would not have had to ask who is calling in the first place, so answering "It's me!" or "I am!" would not be helpful.

As a standard greeting, "Hello. Who is calling?" is very unusual where I live. Just "Hello?" is standard. (Of course, these days, with Caller ID, I usually know who's calling.)
I agree with Clive. I should just state my name to avoid confusion. However, these days, with caller ID, asking 'Who's calling?' is unlikely, in the first place.

Thank you, guys, for your responses. Great help.