How do I get translated strings into Drupal.locale.strings?
Drupal handles populating the needing strings into the javascript object. Much like the entire collection of strings isn't loaded on every page, only the needed strings are added to the JavaScript.

I believe this is done by traversing the script files before they are actually added to the page.

So if you add Drupal.t('Some string'); to your JavaScript code, you should be able to translate that in the translate interface.