On all site

For Likes

elgg_unregister_plugin_hook_handler('register', 'menu:entity', 'likes_entity_menu_setup');

For Delete and Access

elgg_unregister_plugin_hook_handler('register', 'menu:entity', 'elgg_entity_menu_setup');

elgg_register_plugin_hook_handler('register', 'menu:entity', 'my_entity_menu_setup');

 

function my_entity_menu_setup($hook, $type, $return, $params) {
    if (elgg_in_context('widgets')) {
        return $return;
    }
    
    $entity = $params['entity'];
  
    $handler = elgg_extract('handler', $params, false);

   if ($entity->canEdit() && $handler) {
        // edit link
        $options = array(
            'name' => 'edit',
            'text' => elgg_echo('edit'),
            'href' => "$handler/edit/{$entity->getGUID()}",
            'priority' => 100,
        );
        $return[] = ElggMenuItem::factory($options);
    }

    return $return;
}

On Blogs only

Another way:

elgg_register_plugin_hook_handler('register', 'menu:entity', 'blog_setup_entity_menu_items');

function blog_setup_entity_menu_items($hook, $type, $value, $params) {
    $handler = elgg_extract('handler', $params, false);
    if ($handler != 'blog') {
        return $value;
    }

    foreach ($value as $index => $item) {
        $name = $item->getName();
        if ($name == 'access' || $name == 'delete' || $name == 'likes') {
            unset($value[$index]);
        }
    }

    $entity = $params['entity'];

   if ($entity->canEdit() && $handler) {
        // edit link
        $options = array(
            'name' => 'edit',
            'text' => elgg_echo('edit'),
            'href' => "$handler/edit/{$entity->getGUID()}",
            'priority' => 100,
        );
        $value[] = ElggMenuItem::factory($options);
    }

    return $value;
}

Thanks @rivervanrain for taking time, much appreciated. I have just made this to work. The 2nd approach worked for me. Thanks a lot .