One possibility is that your chainring isn't round at all so your setting the tension at the widest part and, when you get to the narrowest part of the ring theres slack there.

However, I would say its most likely that your wheel is moving in the track ends/dropouts. Not too sure about the horrible noise part though - that maybe the chain tug shrieking as its being asked to do all the work.

Some hubs have notoriously bad track nuts that just don't do jack. I would probably upgrade your nuts if they came with a cheap hub. Other options are to rough the paint around the ends/dropouts so the surface isn't so smooth or try with a friends wheel to see if you have the same problem.

If this is an Alu frame be careful about cranking down your nuts too tight.