Using different po/mo files to display different languages


How would I go about showing my one theme in different languages, if I run a multisite with three different websites in three different languages?

I'm referring to the themes .po/mo files.

1. I would like to display the en_US theme file for the English website.
2. I would like to display the da_DK .po/mo theme file for the Danish website.
3. And I would like to display the es_ES .po/mp theme file for the Spanish website.

I'm currently using the WPML plugin, but it really doesn't work properly on my website since the back-end changes doesn't take place on the front-end, so I think the multisite option would be my best alternative option.