possession. First, he says that the former owner of the property gave him permission to live there. The property then sold, and the current owner wants him off.

The statutory period for adverse possession in NH is long - 20 years . He said he's been living there for 24 years, so there's a possibility he could sustain an adverse possession claim. However, if part of that time the use of the property was permissive, then during those times it wasn't "adverse" (i.e., hostile or notorious). So there are some problems with an adverse possession claim.