How to tell a theme to use different .mo and .po files?

There are already an en_US.po file in the theme you are using. You can simply make a copy of that file and rename it as pl_PL.po. You can now open the pl_PL.po template with poedit, do all your translations in there, and just save it. Poedit will automatically create a pl_PL.mo template.

No need to go through all the pt. Just remember, as previously stated, change the language in the wp-config.php to pl_PL