Display all posts under child sub category in sidebar on post page?

I guess you could take a big step using wp_list_categories() with a walker to add a additional Unordered List to every item.

The code:

$cat_id = get_query_var( 'cat' );
$subcats = get_categories( 'child_of=" . $cat_id ); // child categories

class Cat_Walker extends Walker_Category {
    function end_el( &$output, $page, $depth = 0, $args = array() ) {
        $posts = get_posts( "cat=" . $page->term_id );

        if ( sizeof( $posts ) > 0 ) {
            $output .= "<ul>';

            foreach ( $posts as $post ) {
                $output .= sprintf( '<li><a href="https://wordpress.stackexchange.com/questions/89959/%1$s">%2$s</a></li>', get_permalink( $post->ID ), $post->post_title );
            }

            $output .= '</ul>';
        }

        $output .= '</li>';
    }
}

foreach ( $subcats as $subcat ) {
    $subsubcats = get_categories( 'child_of=" . $subcat->term_id ); // sub child categories

    foreach ( $subsubcats as $subsubcat ) {
        $args = array(
            "title_li'         => '',
            'show_option_none' => '',
            'taxonomy'         => 'category',
            'child_of'         => $subsubcat->term_id,
            'walker'           => new Cat_Walker( )
        );

        wp_list_categories( $args );
    }
}