All three of those words are pretty rare. "Long" and "pine" sound very poetic, and I don't think I've ever heard anyone say it in daily life unless they were being melodramatic.
The other one, hanker, is the opposite: it sounds like something an uneducated farmer would say. For me, using any of those words in daily speech is something I would only do if I were trying to be funny.
The meaning is essentially the same, except "long" and "pine" are closer to "want", and "hanker" is closer to "need".