The 6-50 plug has two hots and a ground. So I get 110 between either
of the hots and ground, and 220 between the two hots.

I haven't measured what the L14-20 conector puts out yet, but it should
be pretty much the same, but I have this extra neutral wire. Not quite
sure where to hook this up. I don't know if it would be a good idea to
leave it unconnected. If there is no power comming on the neutral line
(which their shouldn't be right?) I could connect it directly to
ground. Any comments on this?

Thanks.