Well, it seemed like you made my day, David. But now all the strings are back in the cache.
I deleted all local files with customizations. I downloaded a backup though, while I wanted to keep a few strings in a few files, so I uploaded these files only with those entries, after having purged Language string cache. Then all my just deleted strings did pop up again like a jack-in-the-box
I am assuming you refer to "Language string cache" definition at Site administration ► Plugins ► Caching ► Configuration.
Yes, exactly. I have not configured it, so it has default settings.