Anchor only wp_nav_menu

You already mentioned in your question that u had removed li from the menu. so may be this will work. in this walker u can give the class in the Appearance ->menu css options (On the top right of the screen click on ‘Screen Options’ on the bottom row – make sure ‘CSS Classes’ is checked.)

    class Class_Name_Walker extends Walker_Nav_Menu
     {
    /**
     * Start the element output.
     *
     * @param  string $output Passed by reference. Used to append additional content.
     * @param  object $item   Menu item data object.
     * @param  int $depth     Depth of menu item. May be used for padding.
     * @param  array $args    Additional strings.
     * @return void
     */
     function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 )      {
    $indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';

    $class_names = $value="";

    $classes = empty( $item->classes ) ? array() : (array) $item->classes;
    $classes[] = 'menu-item-' . $item->ID;

    $class_names = join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item, $args ) );
    $class_names = $class_names ? ' class="' . esc_attr( $class_names ) . '"' : '';

    $id = apply_filters( 'nav_menu_item_id', 'menu-item-'. $item->ID, $item, $args );
    $id = $id ? ' id="' . esc_attr( $id ) . '"' : '';

    $atts = array();
    $atts['title']  = ! empty( $item->attr_title ) ? $item->attr_title : '';
    $atts['target'] = ! empty( $item->target )     ? $item->target     : '';
    $atts['rel']    = ! empty( $item->xfn )        ? $item->xfn        : '';
    $atts['href']   = ! empty( $item->url )        ? $item->url        : '';

    $atts = apply_filters( 'nav_menu_link_attributes', $atts, $item, $args );

    $attributes="";
    foreach ( $atts as $attr => $value ) {
        if ( ! empty( $value ) ) {
            $value = ( 'href' === $attr ) ? esc_url( $value ) : esc_attr( $value );
            $attributes .= ' ' . $attr . '="' . $value . '"';
        }
    }
    $item_output = $args->before;
    $item_output .= '<a'. $attributes .$class_names.'>';
    $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
    $item_output .= '</a>';
    $item_output .= $args->after;

    $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
}

/**
 * @see Walker::end_el()
 * @since 3.0.0
 *
 * @param string $output Passed by reference. Used to append additional content.
 * @param object $item Page data object. Not used.
 * @param int $depth Depth of page. Not Used.
 */
function end_el( &$output, $item, $depth = 0, $args = array() ) {
    $output .= "\n";
}
}

This walker will add the li classes to a tag. In your theme file (where your wp_nav) is you have to add a custom walker.

<?php wp_nav_menu( array('walker' => new Class_Name_Walker ) );?>

EDIT :

To add the nav-active class to the current menu item, add this extra filter to functions.php

add_filter('nav_menu_css_class' , 'special_nav_class' , 10 , 2);
function special_nav_class($classes, $item){
     if( in_array('current-menu-item', $classes) ){
             $classes[] = 'nav-active ';
     }
     return $classes;
}