The file with the ~ is a backup file that automatically gets created when you save a file. The #readme.txt# is the file being currently edited/in use (i.e., the autosave version). That will usually go away (unlike the ~ file) when you exit emacs normally (if it crashes or gets killed the # files may stay around).
You might find this page about emacs backup files of interest, and this SO question: How do I control how Emacs makes backup files?
You can prevent backup files from being created with this:
(setq make-backup-files nil)