Wangxian being an IEE/SLI dual pair is obvious, but I would also accept ILE/SLI! And I think a really convincing argument could be made for them as IEE/LSI conflictors, although I could never bring myself to believe it.

Now, in earnest:

Wei Wuxian - IEE
Lan Wangji - SLI

Jiang Yanli - SEI
Jiang Cheng - He's my favourite but my read on him isn't great. Maybe LIE; I think a benefactor relationship between him and Wei Wuxian makes sense. I'd also buy EIE.
Madam Yu - Jiang Cheng and Madam Yu are supposed to be virtually identical, so whatever type Jiang Cheng is, Madam Yu is probably that type.
Jiang Fengmian - LSE

Wen Ning - SEI
Wen Qing - Rational NiSe-valuing type. LSI?
Wen Chao - Very one-dimensional Beta villain, lol

Lan Xichen - ESE
Lan Qiren - LSI

Jin Guangyao - IEI
Nie Mingjue - LSI or ESI
Nie Huaisang - Who knows?

Xue Yang - No idea
Xiao Xingchen - EII?
Song Lan - No idea but MXTX mentioned that he has the sense of humour of a rock. Him and Xiao Xingchen being almost-duals but not-quite makes sense to me; maybe LIE.
A-Qing - SEE?