Utsjoki is located at the northern end of the E75 in Lapland, just before the Norway border, and the nearest airport in Finland is in Ivalo (IVL). The nearest airports in Norway are Lakselv and Kirkenes. All of these airports have car rental services.
The closest railroad station is in Rovaniemi, which has a direct bus links to Utsjoki. You can see bus timetables and buy tickets and on the Matkahuolto website
Nuorgam is about 40 km away from Utsjoki along Route 970 which follows the Teno River.