You can drive with a US-registered and tagged vehicle. You will need to have the appropriate liability insurance to drive in the EU/Turkey, and you would need to make sure that your US insurer agrees to coverage for use there. This could be so expensive as to negate any benefit.
Europe.eu outlines what insurance coverage you are required to carry as a tourist, along with other options.
You also need an International Motor Insurance Card, the Green Card for your planned travels in Europe, as well as an International Driver's Permit, carried along with your own State permit.
Mind you, this would be for short-term use and a stay in the area of 6 months or more would subject the vehicle to import regulations and duties. A side note: should it not be a standard transmission, and should you have car problems along the way, it could be difficult to find a qualified shop, and repairs could be rather costly.