Nylon is a silky, thermoplastic material. https://en.wikipedia.org/wiki/Nylon So, is it allowed for men to wear anything made from Nylon, according to Islam? They make leggings, pantyhose, etc. from it. Is it allowed to wear them inside normal socks?
It is halal to wear. As long as it isn't natural silk.
From the wiki you posted:
Nylon was the first commercially successful synthetic thermoplastic polymer
Nylon was intended to be a synthetic replacement for silk
And in accordance with the following Fatwa.
وأما لبس الرجال للحرير الصناعي أو ما أشبهه من النايلون وغيره من الملبوسات الناعمة أو اللامعة... فإنه لا حرج فيه، والحرام هو الحرير الطبيعي فقط؛ فلا يجوز للرجل لبسه من غير ضرورة.
About the men wearing artificial silk or its equivalent like Nylon and similar articles that are soft to the touch or sparkles, there is no issue in it. The Haram is natural silk only, for a man is not allowed to wear it without a need for it.