US Amazon accepts international debit and credit cards. To ship Amazon USA purchases to Sweden, Finland, Norway, Denmark, Netherlands, Belgium, you need a virtual USA address (a real address, not a P.O. box, not an APO/FPO/DPO address).

Freight forwarders (parcel forwarding services) like Shipito will give you a virtual USA address. Some freight forwarders will also allows you to consolidate your packages, so you can save on mailing a lot.

See also:
- Major freight forwarders for shipping packages/parcels from Amazon & other US stores
- Online shops shipping and not shipping to Shipito warehouse in Torrance, CA