Several posts on the web suggest to open the different files you see in ~/Library/Containers/com.apple.Notes/Data/Library/Notes/ renaming them to use the ".html" extension, however I was able to recover them after deleting the ".storedata-wal" and ".storedata-shm" files.
Before proceeding please make a copy of the whole Notes directory. The file(s) with extension ".storedata" is/are what you want to keep and in fact these are sqlite files so you can open them, see the schema and inspect tables with the sqlite3 command.
BTW this happened to me after I started playing with iCloud. My iPhone and MAC notes were not synchronizing anymore and after finding that the iPhone notes were the ones in iCloud I started playing with iTunes and Notes accounts' settings to end up losing my MAC notes and getting those from the iPhone locally. Worth to be said that Notes act funky in terms of synchronization and when they do going to accounts, unchecking and checking back Notes in the MAC solves the issue.