You're nearly there.
The problem is that XPath 1.0 doesn't understand the default namespace that is declared as:
xmlns="http://rep.oio.dk/ubl/xml/schemas/0p71/testpie/"
Try specifying a prefix for this namespace instead such as:
Namespace ns_com = Namespace.getNamespace("def", "xmlns="http://rep.oio.dk/ubl/xml/schemas/0p71/testpie/");
You should then be able to access the node using the following:
org.jdom.xpath.XPath xp = org.jdom.xpath.XPath.newInstance("/def:Invoice/com:ID");