There currently is one option to travel by night train from Bad Schandau (Germany) to Odense (Denmark), taking approximately 10 hours: Namely the RJ 386. These lines are operated by Deutsche Bahn and DSB.
Deutsche Bahn (DB) exited the actual night train business in 2016. However, it operates around a dozen Intercity and Eurocity trains that run exclusively at night.
These trains only have first and second class seats. The cars remain lit throughout the night and the seats cannot be reclined.
DSB, Denmark's national railway, runs passenger trains throughout the country and connecting services abroad.