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:
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 It sounds more natural and modern than the other choices, which would stand out and sound outdated or overly formal.