On the model of translations of country names that end with “-nia” in English, e.g. An Eastóin for “Estonia” and An Mhacadóin for “Macedonia”, I’d expect An Chalafóirn for “California”, which would fit well with Calafóirneach for “Californian”, and thus sa Chalafóirn for “in California”. However, tearma.ie offers California and Calafoirniach for “California” and “Californian” respectively, so it seems as though the Irish translations have not yet taken settled forms.
Very interesting discussion here. From the examples you gave, what I suggested (Caileafóirnia) would be completely wrong. XD
California is the name of a state, though. I'm not so sure it needs a definite article preceeding it. If we were talking about when it was independent for its very short amount of time, though, THEN we'd need it. But since it's a state we're talking about here, I don't see a point for a preceeding article.