The verb is almost never used in speech or writing, but the past participle form is often found as an adjective in the following pairings:
cleft chin
cleft palate
cloven hooves
You would NOT be able to change the word forms in the above phrases. Anyone know any others like this?
Because 'cloven' is most usually found alongside 'hooves', I personally associate a bit of a grotesque or beastly connotation to it, whereas 'cleft' has a more matter-of-fact descriptive connotation.
I'd recommend using 'cleaved' when functioning as a verb in the sentence, e.g. "She had cleaved it." It sounds more natural and modern than the other choices, which would stand out and sound outdated or overly formal.