hello..can anyone advise as to proper bullet diameter for a commercial oberndorf mauser sporting rifle/carbine..caliber marked..."* 8x57 normal".???... thanks for help...

Yes I advise you to slug it and measure it yourself as that is the only way to make sure. Do not rely on anyone else to tell you want the groove diameter of your rifle bore is.
I suspect it is a .318, but you really need to measure it. Get a lead ball, 375 works well, and smack it into the muzzle with a plastic hammer. Measure it.

The "Normal" designation refers to the German standardization process of "Normalization" whereby ammo and chamber dimensions were standardized.
Both the 318 and 323 bores were "normalized".
So to know what the bore diameter is the bore will have to be slugged.

You might take a look at the bottom of the barrel just forward of the receiver. My original Oberndorf Mauser Type S rifle is marked with the bore, groove, and twist dimensions in millimeters there.

I would slug he bore..however there is a cut off date for the .318 bore manufacture and the change to 323, but I don't recall what it is, or that I would trust it as fact, so slug the bore or have your local smith do that for you.

I know some that shot 323 in there 318 bore rifles, some got away with it!! others didn't..Guess it depended on the action..I wouldn't do that! wow think of the Sectional density of that spegetti bullet.