How to get a translated string from a language other than the current one?

To find the answer to this question, you just need to look at how WordPress retrieves the translations. Ultimately it is the load_textdomain() function that does this. When we take a look at its source we find that it creates a MO object and loads the translations from a .mo file into it. Then it stores that object in a global variable called $l10n, which is an array keyed by textdomain.

To load a different locale for a particular domain, we just need to call load_textdomain() with the path to the .mo file for that locale:

$textdomain = 'your-textdomain';

// First, back up the default locale, so that we don't have to reload it.
global $l10n;

$backup = $l10n[ $textdomain ];

// Now load the .mo file for the locale that we want.
$locale  = 'en_US';
$mo_file = $textdomain . '-' . $locale . '.mo';

load_textdomain( $textdomain, $mo_file );

// Translate to our heart's content!
_e( 'Hello World!', $textdomain );

// When we are done, restore the translations for the default locale.
$l10n[ $textdomain ] = $backup;

To find out what logic WordPress uses to determine where to look for the .mo file for a plugin (like how to get the current locale), take a look at the source of load_plugin_textdomain().

So thanks to J.D., I finally ended up with this code:

function __2($string, $textdomain, $locale){
  global $l10n;
  if(isset($l10n[$textdomain])) $backup = $l10n[$textdomain];
  load_textdomain($textdomain, get_template_directory() . '/languages/'. $locale . '.mo');
  $translation = __($string,$textdomain);
  if(isset($bkup)) $l10n[$textdomain] = $backup;
  return $translation;
}


function _e2($string, $textdomain, $locale){
  echo __2($string, $textdomain, $locale);
}

Now, I know it shouldn't be, as per this famous article:

http://ottopress.com/2012/internationalization-youre-probably-doing-it-wrong/

But, I don't know, it works... And bonus: say you want to use it in admin, because the admin language is x, but you want to get/save data in lang y, and you're using polylang. So i.e. your admin is english, but you're on the spanish translation of a post, and you need to get spanish data from your theme locales:

global $polylang;
$p_locale = $polylang->curlang->locale; // will be es_ES
_e2('your string', 'yourtextdomain', $p_locale)