Native English speaker here; I don't think it is wrong to omit "nor" for items before the last one. For example, this is by Rudyard Kipling:
"But there is neither East nor West, Border, nor Breed, nor Birth, When two strong men stand face to face, though they come from the ends of the earth!"
And here's William Shakespeare:
"You know neither me, yourselves nor any thing"
It sounds strange in this sentence, but "she" as a standalone isn't incorrect as a rule.
Normally you would say either "she and I" or "me and her", and it only sounds strange because the order in this sentence is like "I and she" which is backwards.
(I've used "and" instead of "nor" to simplify the examples.)
I have a translation test text for soon-to graduate students of EN philology of certain PL universities that include an ani-ani-ani structures, and none make a meaningful translation because, like here, they insist on a neither-nor-nor structure. IT DOES NOT WORK, YOUR TEACHERS ARE WRONG. You need something like: 'Not I, not you and not she', but even then we are still breaking the "who's she, the cat's mother?" rudeness rule.
Complaint: nor I was accepted as a sentence or a standalone clause in a previous answer but here you have to start with neither.
Why is this so complicated? Here is a quote from WH Fowler that goes some way to explaining:
"Complications occur when, owing to a difference in number or person between the subject of the neither member & that of the nor member, the same verbform or pronoun or possessive adjective does not fit both."
In the example, the person changes from first (ja) to second (ty) and third (ona). To get round it, and make the same teaching point, an example might be:
Ani konie, ani słonie, ani owce (nie jedzą mięsa, na przykład).
That would only work for a pair of people, not a group (which would be 'none of us'). And no, neither can refer to anything not just people, but only for two items (after which nor must be used to include another item).
•"Have you tried refreshing the page or restarting the computer?"
•"Yes, but neither worked!"