From the picture could the longer thing be a side of pocket knife handle? The big ring thing looks like it was attached at the small spot and the big ring was to tie rope or straps on. Maybe for oxen or wagon? I am probably wrong but trying.
Agree on the knife handle, and I think k1ddo on track with the ring, my two cents thinks it's horse/mule tack related, probably yoke, outside chance it's a piece of a busted bit, but most likely yoke. Could be CW knife and ring, let us know if you find more! I'm with you on the other two items