I apologize for any errors in my pictures or writing. My first post.
The first two images look like banded calcite to me. The rock appears to have distinct cleavages, no clearly conchoidal fractures, and a slightly waxy luster on the weathered surfaces. Sometimes this type of rock goes under the term onyx but traditionally onyx is a type of chalcedony. If it is banded calcite a typical knife will easily scratch the surface, additionally it would fizz with some muriatic acid (or dilute HCl). If it is type of chalcedony, then knife will have a harder time scratching the surface an may not if the knife is on the soft side. Also the acid will not react with the stone.
Jan Doggen's suggestion will help you get better results for the other stones.
First and second one seems to be chalcedony (because it's banded). Igneous. Unlikely, metamorphic.
Third and fourth picture apparently have garnets (the red dodecahedrons). I'm betting my buttons it's a metamorphic rock.
(more experienced fellas, please correct me if I got something wrong - I'm still learning)
Quarts and most of all agate. Where did you find them? That was just my guess.