Setting Wordpress language programmatically?

I came up with following solution as I needed to generate invoices from a plugin in different languages in the scope of the same request:

    global $locale;

    $locale = 'en_CA';
    load_plugin_textdomain('invoice', false, 'my-plugin/languages/');
    generateInvoice(); // produce the English localized invoice

    $locale = 'fr_CA';
    load_plugin_textdomain('invoice', false, 'my-plugin/languages/');
    generateInvoice(); // produce the French localized invoice

I found a different solution:

// Set user selected language by loading the lang.mo file
if ( is_user_logged_in() ) {

    // add local filter
    add_filter('locale', 'language');

    function language($locale) {
        /* Note: user_meta and user_info are two functions made by me,
           user_info will grab the current user ID and use it for
           grabbing user_meta */

        // grab user_meta "lang" value
        $lang = user_meta(user_info('ID', false), 'lang', false); 

        // if user_meta lang is not empty
        if ( !empty($lang) ) {
           $locale = $lang; /* set locale to lang */
        }

        return $locale; 
    }

    // load textdomain and .mo file if "lang" is set
    load_theme_textdomain('theme-domain', TEMPLATEPATH . '/lang');

}

Via: http://codex.wordpress.org/Function_Reference/load_theme_textdomain

I guess you're looking for the override_load_textdomain filter, called just in the beginning of a load_textdomain function call.

That would be something like:

function my_load_textdomain ($retval, $domain, $mofile) {

    if ($domain != 'theme_domain')
        return false;

    $user = get_currentuserinfo()
    $user_lang = get_user_lang($user);

    if ($new_mofile = get_my_mofile($user_lang)) {
        load_textdomain('theme_domain', $new_mofile);
        return true;
    }

    return false;
}
add_filter('override_load_textdomain', 'my_load_textdomain');

Code from brain to keyboard, not tested. You should do some more validations and so.

Since WP 4.7 you can use:

switch_to_locale('en_US');

Reference: https://developer.wordpress.org/reference/functions/switch_to_locale/