While the most difficult part of bringing a car over from the states is shipping, importing guns is more complicated. Icelandic legislation requires gun owners to hold a firearms permit, unless the weapon has been permanently deactivated by a gunsmith.
To own a gun in Iceland, you must be at least 20 years old with no criminal record. You must pass a mental and physical health check and get recommendations from two people to attend a course on guns, gun safety, and gun and hunting laws. After passing a written test, you’re issued a permit for smaller shotguns and rifles. For larger rifles (up to 30 calibres) and semi-automatic shotguns, you must wait an additional year.
It’s prohibitedto import automatic or semi-automatic handguns to Iceland; automatic or semi-automatic rifles; automatic shotguns; and semi-automatic or manually loaded multi-cartridge shotguns with chambers for more than two cartridges, unless the weapon has been modified to comply with these conditions. Importing firearms without a manufacturer’s serial number is prohibited, but this condition can be waived when a firearm has a collectible value. Collector permits can be issued for the possession of collectible firearms with historical value.
As for cars, all imported vehicles must be cleared through customs and examined in an accredited inspection facility, and finally registered with the Icelandic Transport Authority.
You may also find the more recent Ask Iceland Review on importing guns to Iceland to be useful!