I really don't understand this part.
 

Nagoyankee, I've given a look at the sentences after this (the Kobutori's story starts again) and I've understood it but this sentence I really can't understand. could you help me, please?

このへんで、日本百科事典でも、ちょっと覗いてみると 、私もたちまち老幼婦女子の尊敬の的たる博学の士に一 変して、（世の物識りというものは、たいていそんなも のである）しさいらしい顔をして、鬼について縷縷千万 言を開陳できるのでもあろうが、

I had understood the previous sentences and after 開陳できるのでもあろうが is repeated a sentence that appeared at the beginning so I know what is written in it. But this part, particularly 私もたちまち老幼婦女子の尊敬の的たる博学の士に一変 して, I can't understand. I've tried but I don't understand it, even because words such as 老幼婦女子 or expressions as 士に一変して, well the truth is that I've not found them in the dictionary.

I don't expect to solve all your problems, not to take away the job of helping from someone who is for sure much more competent than me (and mind that I might completely wrong in what I say).

However for the couple of word you said you cannot find in any dictionary:
老幼婦女子 mean "old and young, women and children"
while 一変 means a complete change. I have had a couple of native speakers confirming this and a couple denying, so take it the way you want, but the 一 used alone has the same meaning of 一番...from here the biggest change (sorry to the rest of the forum, but I don't know this in English, it means also dietro-front).
Then to Nagoyankee the easy (for him LOL) job to fill the huge amount of blanks I have left.

たちまち = in no time
老幼婦女子 = a literary expression for "everyone"
尊敬の的 = the target of admiration
たる = an old form of である
博学の士 = a man of erudition, a well-read man
一変する = to turn entirely into something else

私もたちまち老幼婦女子の尊敬の的たる博学の士に一変 して = I, too, would turn into a man of erudition in no time who is the target of everyone's admiration.

I'm certain that you have no problem with 「このへんで、日本百科事典でも、ちょっと覗いてみる と」.

（世の物識りというものは、たいていそんなものである ） means "as I'm sure that all well-read mean are like that." This phrase modifies the rest of the phrase that follows.

しさいらしい顔をして、鬼について縷縷千万言を開陳で きるのでもあろう = I would be able to state openly and fearlessly my views on 'oni' in a highly self-important manner.

As always, thank you very much Nagoyankee.
I hadn't found the word 老幼婦女子 but the word divided in
老幼 old and young
婦女子 woman, wife
so I was a little confused about it.
Then I hadn't thougt to 博学の士 as a single word but to
(博学)の士に一 変して
But I didn't understand it and now I know the reason.
How I was wrong about that.
Thanks again