I can select posts via my custom taxonomy as explained in the codex. But I am not sure, how I have to set up the tax_query if I want to get only posts which have no relation in the custom taxonomy at all. Any suggestion?

2 Answers
I have found an answer by myself, for those landing here by google:
$taxq = array(
array(
'taxonomy' => 'story_lng',
'field' => 'id',
'operator' => 'NOT EXISTS',
)
);
That results in
AND (NOT EXISTS( SELECT
1
FROM
wp_term_relationships
INNER JOIN
wp_term_taxonomy ON wp_term_taxonomy.term_taxonomy_id = wp_term_relationships.term_taxonomy_id
WHERE
wp_term_taxonomy.taxonomy = 'story_lng'
AND wp_term_relationships.object_id = wp_posts.ID))
AND wp_posts.post_type="story"
AND (wp_posts.post_status="publish"
OR wp_posts.post_author = 1
AND wp_posts.post_status="private")
wich is basically the same as Pieter Goosen suggested, but merged in one query (and fewer lines of code).