Well, usually I don't care much about licensing my code and consider anything I've written myself to be public domain or BSD or whatever the most premissive license that works where you live is. However, parts of The Unarchiver are based on libxad, which is LGPL 2.1 (and, apparently, "or later") and I haven't kept close track of which files could be considered entirely my own and which are derivative of libxad code, so the safest is to just assume everything is LGPL.
The Unarchiver already is built around a core library, though, so there's not much work to be done there. It should be entirely possible to use it in another project. Documentation is sorely lacking, though. There is a short overview on the wiki and that is all. Hopefully it is self-descriptive enough that it shouldn't be too hard to use.