The wires would indeed be 10 AWG.
Wire nuts, properly applied and preferably taped so they won't vibrate loose, are a perfectly acceptable way of securing the connections. I would tend to trust those over garden variety crimp-on connectors. Putting that in a weathertight box would be A-OK and I think required by code if exposed to the elements or road spray outside. If inside, a plain ordinary electrical box would suffice.
(I also suspect you don't actually mean cast iron junction box; I've never seen such a beast!)
