Originally Posted by well biked
It appears from the photos the dropout is bent in two different ways, with the space where the axle slides in being spread apart more than it's supposed to be, and also the face of the dropout is bent inward. When I said "align the dropout" I was referring to the face of the dropout being aligned, I really didn't mention anything about the other issue, although I should have. I think to get smooth, reliable shifting, even with friction shifters, you'll need to align the face of the dropout, and of course you'll also have to bend the dropout back so that the space where the axle goes is the correct dimension for the axle nut to be tightened down against it. And then you'll still need a new adapter claw, unless you can bend that back, too-
I thought it looked bent 2 different ways as well. Sorry to say but the frame looks pretty cheap with just the basic dropouts and no built-in ear for the rear derailleur. Unless the frame holds a lot of sentimental value I wouldn't hesitate to give it a go in my own shop. If you have a big machinist vice securely mounted to a bench you could mash the dropout face flat, then once very tight, just bend the rest of the frame as the dropout remains stationary in the vice. Eyeball it until it appears parallel to the front fork dropouts or until your derailleur pulleys are in line with the freewheel cogs with the derailleur remounted.
You're going to need to close that gap where the drop out opens downward. How in the world did it get that way BTW? Not sure how to achieve that. If you were successful with the vice technique I might even go back to the vice and try to carefully close that gap. If not, you could always take a hammer and a big drift pin and whack on it until it submits. Those dropouts look stamped, not forged which to me means they are somewhat maleable.
Just had to ask, What's the deal with the funky handlebars?
Good luck.