Are there any side-effects of using multiple string.xml files?

As stated in the documentation you can use whatever filename you want:

The filename is arbitrary. The <string> element's name will be used as the resource ID.

There may be negligible side effects in performance, you can add as much as you can. I have 3 activity files MainActivity, PhotoActivity, UserActivity, create a common strings.xml file and other activity related files.

-strings.xml                    -> create common string values here.
  --strings_main.xml            -> create main activity specific string values here.
  --strings_photo.xml           -> ...
  --strings_user.xml            -> ... etc etc

Hope this is helpful. Thanks!