Insolvable, insoluble, and unsolvable

I don't think there's any possibility of a semantic distinction in the context of problems. The only difference worth pointing out is that insoluble is far more common...

This isn't to say that either of the alternatives are "incorrect", though I personally don't like insolvable (it's just a relatively uncommon/dated negated form). And in fact there's some justification for preferring unsolvable simply because insoluble has another well-known sense...

insoluble [of a substance] - that cannot be dissolved [often, in water]

...but since that sense can't possibly apply to problems, there can be no ambiguity here.