Can Norwegian passport holders apply for VOA in Shenzhen?

Norwegians can definitely apply and obtain a Shenzhen VOA, but only if arriving to Shenzhen from Hong Kong or Macau. Anyway, you should be aware that a Shenzhen VOA is limited to only Shenzhen city limits.

By the way, Norwegians are eligible for 24 hour visa free transit. So, they can travel through China using 24 hour visa free transit, but they cannot use 72 and 144 hour visa free transit.