Jack - it may be your ammo. There is not a lot of new manufacture 8mm ammo out there and a lot of the mil-spec stuff is old, very old and not reliable. An example is some turk 8mm a buddy got for his VZ-24 - it went bang, boom, spittzle, bamp, no-fire, etc. Some of the 'Original' WWII stuff should be strictly for display - some of the stuff made in the 50s in the comm-bloc nations is also not very good. About the best surplus stuff around is the Portugese mil-surp - it is reloadable, accurate and reliable. Try some new stuff by S&B - that should work fine for you too.
Also, repost this on the Mil-Surp site - you will find a lot of advice there about ammo preferences for some of those older K98s and advice about making certain she functions properly for you.
At the onset, if some of that stuff is hard to chamber, I would dump it. Your K98's chamber won't tighten up after all these years unless it is rusted or badly pitted and holds onto the brass as a result, which you have not said happens. Headspace will cause cases to separate, which you have not said happens. Sounds like bad ammo to me. If you think you need a new firing pin there are tons available. HTH. Mikey.