In general, I would take "funny sort" to be a common euphemism for being of eccentric behaviour, suggesting some mild mental derangement. It could have different connotations, but from the story it seems eccentricity was what was meant.
"funny" has two basic meanings, as per OED:
1 Causing laughter or amusement; humorous.
‘a funny story’
‘the play is hilariously funny’
2 Difficult to explain or understand; strange or odd.
‘I had a funny feeling you'd be around’
‘it's a funny old world’
‘I do get some funny looks’
‘the funny thing is I can't remember much about it’
‘that's funny!—that vase of flowers has been moved’
Now, the phrase "a funny sort" in turn, as far as I know, only refers to the second meaning of "funny". I only found one place where this was discussed, and nowhere where it was defined.
However, if you Google it as a phrase, you only find it with the meaning "strange" (at least that's what my results showed):
A funny sort of welcome.
Complex new visa and immigration regulations are in danger of sending out the wrong message to foreign students and academics, reports Melanie Newman
A funny sort of democracy.
Around the world, Washington endorses then deposes rulers
I have never ever hear or read anything where "a funny sort" would denote something humorous. Even if the context would suggest it (as I believe, it doesn't, in the JKJ story), if we were speaking about, let's say, a play:
-- What was the play like?
-- It was a funny sort of play.
I would presume the speaker means it was a strange one.