Suppose that "intransitive" means "lacks a surface object". And suppose that "unaccusative" means "has a subject that begins in object position," and "unergative" means "has a subject that begins in the same position as a transitive subject."
Then I can think of two imaginable kinds of intransitive verbs that are neither unaccusative nor unergative, though whether either of them is attested I don't know.
One would be a verb with neither an underlying subject nor an object. Verbs like 'rain' (as in, "it's raining") might be candidates for this, depending on what we thought about the word 'it' in that kind of sentence.
Another would be a verb with an underlying subject that began in some position other than the usual ones for transitive subjects and objects. So called 'psych-verbs', which have meanings like 'worry', 'be bored', etc., might be a candidate for this kind of verb; in many languages, such verbs assign odd cases to their subjects, so they are unusual in at least that respect.
How these kinds of verbs behave with respect to classic unaccusativity diagnostics would be a natural next question, to which I don't know the answer. It might be worth looking at Levin and Rappaport Hovav's classic 1995 book 'Unaccusativity'.