Using several add_action with parameters inside a class

The init action…

is one of many WordPress core action hooks. Hence it does not require, i.e. should not be accompanied by, a manual do_action call.

You only need to manually run do_action for custom, previously non-existent, action hooks.

Further, init is not the action which you want to hook the script enqueuing with. There is an action specifically for this purpose.

Your situation

if ( ! class_exists( 'WPSE_Your_Class' ) ) :
class WPSE_Your_Class
{

    private $enqueued = array();

    public function enqueue_all_scripts()
    {
        if ( is_array( $this->enqueued ) && ! empty( $this->enqueued ) ) {
            foreach ( $this->enqueued as $script ) {
                wp_register_script(
                    $script['handle'],
                    $script['src'],
                    array( 'jquery' ),
                    $script['version'],
                    true
                );
                wp_enqueue_script( $script['handle'] );
            }
        }
    }

    public function __construct( $enqueued = array() )
    {
        $this->enqueued = $enqueued;
        add_action( 'wp_enqueue_scripts', array( $this, 'enqueue_all_scripts' ) );
    }

}
endif;

Pass the $enqueued array to the object instance via the constructor of your class.
Assign that value to a class property and thereafter hook the enqueue_all_scripts method to wp_enqueue_scripts.
Make said method dependent on the previously populated class property.

Create a new instance like so:

$enqueued = array(
      array(
           'handle' => 'some-handle',
           'src' => 'http://some-url.com/path/to/script/scripts.js',
           'version' => '1.0'
      ),
      array(
           'handle' => 'another-handle',
           'src' => 'http://some-url.com/path/to/script/another_scripts.js',
           'version' => '1.1'
      )
      // possibly more
);
$your_class_instance = new WPSE_Your_Class( $enqueued );

Sidenote

As an aside, &$this is PHP4, and, as I recently learned, it is useless to attempt to support PHP4, since the core won’t run on it anyway.

Edit – your full code rewritten

The above is the way I’d do it. That’s certainly not the only option and most likely not the slickest possible, but it does work. Given your edit, I’ve adjusted your code while trying to preserve some of your own naming conventions and coding style:

class Nomade
{

    /* class properties */
    private $enqueued = array();
    private $features = array();
    private $menus = array();
    private $styled = array();

    /* constructor */
    public function __construct( $menus, $features, $enqueued, $styled )
    {
        // Assign values to class properties
        $this->enqueued = $enqueued;
        $this->features = $features;
        $this->menus = $menus;
        $this->styled = $styled;

        // Define base constants
        define('THEME_FRAMEWORK', 'nomade');
        define('NOMADE_VERSION', '1.0');

        // Define directories
        define('NOMADE_DIR', get_template_directory());
        define('NOMADE_LIB_DIR', get_template_directory() . '/library');

        $this->AddThemeSupport();
        $this->MenuBuilder();

        // Add support for WordPress features
        add_action( 'after_setup_theme', array( $this, 'MenuBuilder' ) );
        add_action( 'after_setup_theme', array( $this, 'AddThemeSupport' ) );
        add_action( 'wp_enqueue_scripts', array( $this, 'EnqueueScripts' ) );
    }

    public function AddThemeSupport()
    {
        if( is_array( $this->features ) && ! empty( $this->features ) )
        {
            foreach ( $this->features as $feature ) {
                add_theme_support( $feature );
            }
        }
    }

    public function MenuBuilder()
    {
        if( is_array( $this->menus ) && ! empty( $this->menus ) )
        {
            register_nav_menus( $this->menus );
        }
    }

    public function EnqueueScripts()
    {
        if( is_array( $this->enqueued ) && ! empty( $this->enqueued ) )
        {
            foreach ( $this->enqueued as $value ) {
                wp_enqueue_script(
                    $value["name"],
                    $value["location"],
                    array("jquery"),
                    $value["version"],
                    true
                );
            }
        }
    }

}