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".

I'd agree with Johnny about 'hanker'. It's quite a rare word. 'pine' is also quite rare. It means becoming unhappy or ill because you miss something or someone. 'long' is a little more common. If you 'long' for something you are looking forward to it. For example, 'I've been working for months without a break. I'm longing for the holidays.'