The 8x56R Hungarian is not the same as the German Mauser 7.92x57JS round.  (Note: the JS stands for heavy ball, spitzer bullet, .323 diameter -- early cartridges for the Mannlicher M1888 rifle had .318 diameter bullets.) 

 

The Original Steyr M95 rifles and carbines were chambered for an 8x50R cartridge.  They were produced from 1897-1918 by Steyr for the Aurstrian-Hungarian government.  From 1930-1940, the rifles and carbines on hand were rebarreled and modified to the 8x56R cartridge. 

 

Like the 8x50R, the 8x56R is a rimmed cartridge.  The 8x50R cartridge takes a .323 diameter bullet; the later 8x56R cartridge takes a 209 grain, .329 diameter bullet.  Fresh ammunition is difficult to get.  Brass for boxer primers is available for hand loaders from Old Western Scrounger. 

 

The Steyr Model 95/30 rifles are 5-shot, stright-pull bolt actions and a very fast action to operate.  The problem is getting fresh ammunition.  Hornaday makes new JSP ammunition, but it is expensive at $24 for a box of 20 rounds.  Most military surplus ammo dates from the 1930s and early 1940s.  This stuff has corrosive primers and cannot be considered reliable.  It would be suitable for breaking into components for reloading.  Remember: rifle + ammo = shooting fun; rifle - ammo = club.

I'm not really sure, sorry.

The Model 95/30 is a very nice rifle and the straight-pull acton makes it very fast.  The 95 is loaded from a 5-round en bloc clip -- like the U.S. M1 Garand rifle -- that stays in the action while firing the five rounds.  That is, the clip holds and positions the rounds for feeding by the follower.  On the last shot, it falls out the bottom of the rifle and you're ready to reload.

 

It may take some scrounging to find ammo, but the Steyr is a very will finished rifle that has all the old world's craftsmanship of the turn of the 20th century.  Most Steyrs are in excellent shape.  Do some scrounging around at gun shows and on the internet and you'll find ammo.  The 30's and 40's Hungarian has a pretty good reputation for functioning.  The German production stuff is mostly good and usually comes with the 5-round clips.  If you can't get the ammo with clips, there are several places that sell them.

 

The Model 91/30 Mosin-Nagant is more common a rifle and the 7.62x54R ammunition is easier to find.  However, the M-N is pretty clunky in comparison to the Steyr.  The M-N is superior because, unlike the Steyr, it does not need an en block clip to feed its 5 rounds from the magazine.

The Swiss K-31 is another straight pull bolt action that is reasonable accurate.  Ammo is available for them as well.  The 7.5 mm Swiss round uses .308 diameter bullets too, so if you reload, even better.