Generating a perfect loop

That’s because you’re looping twice due to the while. Completely unecessary.

foreach ($orders_ids as $details) {
    $order = wc_get_order($details->order_id);
    $fornavn = $order->get_billing_first_name();
    $etternavn = $order->get_billing_last_name();
    $deltakerkategori = $order->get_meta( '_billing_field_447', true );
    $deltakerradio = $order->get_meta( '_billing_field_538', true );
    echo ''.$fornavn.' '.$etternavn.' '.$deltakerkategori."https://wordpress.stackexchange.com/".$deltakerradio.'<br>';
}

Additionally, if that doesn’t fix it due to…well, magic, try this patch:

foreach( array_unique( $order_ids ) as $details )

But this smells. Bad. Check your data and see where it’s going wrong.