To be a bit nitpicky, the main sentiment here is クセの強さがあります, which is saying that the person in question is a highly (lit. strongly) eccentric/idiosyncratic one. It's not saying that her tendency to spew invective itself is strong, or something that she "always" does.
You can tell because the sentence specifically says たまに, which suggests that it's a rather infrequent occurrence (which in turn probably makes it even more shocking/suprising when she does).
You could render it as something like "[She's] a highly eccentric/idiosyncratic character who has a tendency to spew extreme vitriol [at others] from time to time."
(I say "character" because the line in question appears to be from this page describing a character in a movie:
屍人荘の殺人 インタビュー: 神木隆之介×浜辺美波×中村倫也、語り尽くす「屍人荘の殺人」 - 映画.com)