Get current page term title to use in WP_Query

Do what single_term_title does and check the queried object with get_queried_object.

function single_tax_slug() {
  $term = get_queried_object();

  if ( !$term )
    return;

  if ( is_category() ) {
    $term_slug = $term->slug;
  } elseif ( is_tag() ) {
    $term_slug = $term->slug;
  } elseif ( is_tax() ) {
    $term_slug = $term->slug;
  }

  return $term_slug;
}
$slug = single_tax_slug();
var_dump($slug);

If you look at that code, it is basically the first few lines of single_term_title, simplified considerably, and altered to get the slug.