Violet-ISTJ
Klaus-INTP
I think her and her brother are both introverted, and thinkers but I pegged Violet as a sensor just because she seems to have more hands-on pursuits than Klaus. She also seems very Si-dom, she's always thinking back to previous methods and techniques to solve new ones, which is something that frustrated me a bit about her (though I admit Klaus was suspect to doing this to). For instance in the first book she figured out how to save Sunny using that Finnish knot or whatever from, relating back to past experiences (the knot was proven efficient before, hence I should use it again) instead of thinking from a more abstract approach. Klaus I pegged as an N though I'm not really sure if he is Ti-dom or Ni-dom which would put him as INTJ. The only reason I put him as a P is because he seems to lack an ordered way of thinking about things.
Sunny- Exxx
It's kind of hard to type a toddler especially one who doesn't speak properly for most of the series lol. But I think she's more outspoken than her siblings, or maybe it's just the baby talk. But she does seem externally oriented always wanting to chew on something, and having a knack for cooking which I suppose would make her Se dominant, but at the same time I didn't want to rule out Ne-dom just because.
Count Olaf-INTJ
I'm not going to lie, I went by stereotypes here lol. He is quite a bit of a caricature it's hard to not peg him down as some evil mastermind INTJ.
Lemony Snicket- IxFP
The way he is always brooding over Beatrice in a macabre poetic way just seems very F to me. He has a very quiet nature that I think surfaces throughout the series, he's always alone (though that has more to do with the fact that he's on the run from authorities). He just seems like a broody poetic tragic romantic type.
Kit Snicket-XXXX
Honestly I don't know, her character wasn't prevalent enough in the series to peg down enough definite traits
Mr. Poe-ISTJ
Again just going by stereotypes, stuffy, boring banker with no imagination and unwilling to use some, when the kids are trying to explain their dilemmas.
Esme Squalor- ESTJ
Ruthless, does not care about other people unless they benefit her, always scheming and planning. Also is image-conscious, shallow, and vain, and represents some of the worst aspects of an ESTJ. Very bossy, I believe there are times in the series when Count Olaf and his minions,can't even stand her.
Duncan and Isadora and Quigley- Hmmm, I haven't read the series in a really long time so I'm not too sure about the triplets... but if I were to take a quick stab I would say the first two are perhaps F's?