ajax problem – function on server is not called

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 {    
           ...