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Look for .po files, xliff or .property files. There are quite a few standards https://en.wikipedia.org/wiki/Translation_memory

There is desktop software as well as SaaS websites who offer to manage those files with online editors for you. Some have APIs that allow you to pull new translations (or whole files in the format of your choice). It makes it also easier when dealing with external translators or if you're in a hurry and want to pay somebody to translate just one string.

I used http://gengo.com/ in the past but they seem to have gone full enterprise now. https://www.transifex.com/ and https://poeditor.com/ look like good alternatives. I'm sure there are many others.

You can download and install the open source http://pootle.translatehouse.org/. That's what big open source projects like LibreOffice use.