I think this is a Flugelhorn in C by Egid Glassl. The leadpipe takes a regular trumpet mouthpiece, but then it plays in C# (or Db). A previous caretaker has conjured up a tuning bit with adapter to French Horn mouthpiece (and even soldered the mouthpiece into it) to play in C. I have tried some cornet bits that (almost) fit to play in C with cornet mouthpiece. In Germany and Bohemia, the Flugelhorn in C seems to (have) be(en) quite common, so I feel confident to assume that C is indeed the intended pitch for this horn.
There is a large crack in the 1st valve slide, but apart from that and some dents, the horn is in good condition and plays.
Listen to it here: https://www.youtube.com/watch?v=xmkAR9pD0q8