I would recommend Lucy. It comes with a lot of what you want out of the box and has the speed to pile on all the correlated queries you want if you build the data for it to use. For misspellings you’ll need to either apply Text::Aspell (tunable misspelling) or Text::DoubleMetaphone (major misspelling) or similar. Synonyms… not sure, I’ve never done it. If you have a specific domain, there might be prior art, like the UMLS::Similarity stuff for medical knowledge. Not sure about generic thesaurus stuff. Let us know if you figure that piece out.

This stuff is typical but not easy. When you put so much in the mix then ostensibly simple things like sorting can get difficult. This kind of search also works best with either static or slowing slowly changing search bodies. Search here is fast at the expense of indexing the data up front.

Update: recent example—Re^3: Using indexing for faster lookup in large file.