Yup, sounds like you have a corrupted hard disk catalog. The best way to fix this is with a utility called DiskWarrior from Alsoft. At some point your Macintosh has crashed and these mystery files were created on your HD. They show up in your Finder because the catalog says they're there. You can't delete them because they don't really "exist."( A crude analogy would be that the card for the book is in the catalog at the library, but the book has been thrown away). DiskWarrior will scan your drive for errors and rebuild your catalog if damaged.
As an Apple Authorized Technician, I'd rate DiskWarrior as one of the most valuable pieces of software I've ever owned. I use it daily to fix problems on Macintoshes. A corrupted HD catalog can cause all sorts of errors: startup problems, mystery files, undeletable files, and even crashes/freezes. It is, in my opinion, the number one problem (and most common) that Macintosh users face. Fortunately, DiskWarrior makes fixing it easy. It's well worth the small amount of money you pay for it.