How to query wp_postmeta table for any specific meta_value?

$wpdb->wp_postmeta is wrong. Always use just $wpdb->postmeta – without further prefixes.

So…

global $wpdb;

$querystr = "
    SELECT DISTINCT meta_value 
    FROM $wpdb->postmeta 
    WHERE meta_key LIKE 'movie_name' 
    ORDER BY meta_value ASC
";

$movie_names = $wpdb->get_results( $querystr, OBJECT );

if ( ! $movie_names ) {
    $wpdb->print_error(); // Get the last error message for debugging
}
else {
    // Do something awesome with the movies
}