Re: 16gauge/7.7mm double barreled shotgun/rifle value?
OK. Let's take that drilling. The shotgun barrels are 16 gauge, the most common gauge on the European continent. The Crown/W is the proof for choked barrels. There should be a mark for the chamber length in millimeters, but I don't see it. The crown/U is the definitive proof. The "Suhl" mark indicates the location of the proof house.
The rifle barrel is indicated as 7.8mm bore size, which is 8mm; the chamber length is 57mm, so the barrel is for the 8X57JR or JRS. The StmG means Stahlmantel Geschoss or steel jacket bullet indicating that the gun can be safely used with jacketed bullets.
The 15 gram is the bullet weight (sorry, in a private message, I said powder weight, which would be absurd) of 230 grains. The 5823 is probably the serial number, the 10 38 is the date of proof (Oct. 1938). The latter date would seem to be confirmed by the general appearance and engraving of the gun; everything points to a gun of that era.
The barrels are made of Krupp Laufstahl or Krupp Barrel Steel, the best quality barrels.
I have little experience with evaluating those drillings, so will defer to others, or you can look up sales by Googling "Drilling" and checking out sale sites.