There currently is one option to travel by night train from Osnabrück (Germany) to Innsbruck (Austria), taking approximately 11 hours: Namely the UEX 1307 operated by UEX.
UEX (Urlaubs-Express) runs seasonal night trains and car-carrying trains between Germany and Austria.
You can choose a seat, a couchette berth, a whole couchette compartment, a private sleeper compartment or connected sleeper cabins.
You can bring your car, but only between the car terminals, and you book the vehicle along with your ticket.
Skis travel free in the ski compartment. A bistro on board sells drinks and snacks.
Children with their own seat or bed pay a reduced fare.