How can I add different menus (different style menu) on each page?

The easiest would be to serve 2 different menus and assign them different css classes, so you can style them differently.

if ( is_home() ) {
    // use home menu
    wp_nav_menu( array( 'menu' => 'home', 'menu_class' => 'menu_home' );
} else {
    // use other menu
    wp_nav_menu( array( 'menu' => 'nohome', 'menu_class' => 'menu_no_home' );
}

I think, a plugin would make it more complicated than needed.