Without more info, video or pics, it's hard to say what's going on, but based on my reading and experience I'd say the problems you're having are due to: weak welds, which can be fixed with practice; and/or not having the handle in line with the stock while on the anvil, as Josh said, which also can be fixed with practice.
Never heard of using a nut and all thread,but I don't see why that wouldn't work. But if either of the above are contributing, you'll still have the problem.
If you were my son, I'd say, grab a piece out of the scrap pile, go on you-tube to learn the difference between good and bad welds and then spend an hour or so just laying beads in a straight line until you can consistently lay a solid weld. Also, I've never used a flux-core wire feed welder and my buddies who are professional welders say that these machines tend to be cheap and are not easy to learn on.
While not an expert welder by any stretch of the imagination, I can make decent, solid, good looking welds when laying a line, but when I weld a piece of 3/4" square for a handle on a billet, about 40% of the time they look good and 60% they look like crap. But even these look better than when I try to use 3/4" round stock for the handle.