I have files named en_US.po, ru_RU.po etc. Editing *.po files in PoEdit is very useful, but not while adding new strings manually.
How can I easily add new translation strings which are not automatically detected by PoEdit?
You misunderstand how gettext translations work. Source strings for translation are extracted from source code. It doesn't make sense to add them manually — they would never be used if they didn't have corresponding source code that uses them.
So the way to add strings is to use xgettext
or Poedit's update from sources functionality.
P.S. The name's Poedit, not PoEditor.
You can configure your project (*.po file) opened in PoEdit. If you will done that correct PoEdit automatically update what to translate in this opened *.po file.
After that you have to click in Update button and PoEdit will start scan your sources for strings to translate. Then you only have to do is translate found strings.