Actually, the Sonny Bono Copyright Extension Act of 1998 extends the term of copyright to 95 years from the death of the creator, or 120 years from creation (or 95 years from publication) for works created by a company, an author working under a pseudonym, or an anonymous author. Essentially, this assures that NOTHING that is currently copyrighted will enter the public domain before December 31, 2018.
So yes, the Kipling works are still covered by copyright, and the work done by the anonymous author is also covered by copyright, unless the author EXPLICITLY put the work into the public domain.
A little work on Google should help you track down the current holder of the copyright for the Kipling work in question -- you can check the U.S. Copyright office to see if a copyright is registered (probably is), you could also check with the last known publisher. As far as the anonymous work is concerned, you may have significantly more work ahead to find out who owns the copyright. If you use the anonymous work and there is a copyright in existance, you could be sued by the owner for copyright infringement. You can check with the copyright office to see if the anonymous work has a registered copyright.
If you are working with a publisher, they may have resources to help you track down the copyright information for the anonymous work.