On Sat, 17 Jul 2010 18:37:29 -0700 (PDT), rlz wrote:

I have an old handcrank drill (see link for similiar style)

http://ecoble.com/wp-content/uploads...ia-flickr1.jpg

I was thinking of trying to use it with some socket wrenchs. I'm not
sure what this type of drill is called. I've always called it an auger
drill, but I don't know the exact name.

It's called a "brace", as in "brace and bit".

It has two teeth which grabs the drill bits. I was wondering if
someone makes an adapter that would securely fit this drill that has a
3/8" square end for deep sockets

I know this is odd, but I sometimes work out on a farm putting in lag
bolts on fences. My cordless drills seem to die at the worst time.
Utilizing this type of setup would help in a pinch.

Why not just use a 3/8" ratchet wrench? Use the drill to make a pilot hole.
You do drill pilot holes?