I think there are 3 pumice pieces.

Is it running shoes?
Not once, not thrice, but in between.
Found twice

Our loyal companions can be seen.
Again, you can only get 2

With friends by side, and running behind
Well you mentioned running

They really are not hard to find.
Its not too hard to find Hades or Tantarion

"The Bible only names me once!" they say,
Hades was leader of the Underworld. Tantarion is a book like the Bible. Hmmm.

But tell me, friends, what are they?
Dunno, but my best guess is running shoes.