My guess is that the shipping method isn’t initialised when you make an ajax call. Try moving your actions directly into your init function. EG:
function checkAjax(){
print_r($_POST);
exit;
}
function dhlsweden_shipping_method_init() {
//use checkAjax since you don't have access to your shipping method class. If this is the case then you need to rework your code
add_action( 'wp_ajax_checklocation', 'checkAjax' );
add_action( 'wp_ajax_nopriv_checklocation', 'checkAjax' );
if ( ! class_exists( 'WC_Shipping_DHLsweden' ) ) {
class WC_Shipping_DHLsweden extends WC_Shipping_Method {
...