I’ve seen (and used) some pretty wild and complicated tactics to get my back wheel straight in my dropouts. Coming from an age where riders rode brakes and frames were not as forgiving in the back end for tire clearance, a straight back wheel was pretty much a priority, and we used all sorts of techniques to make it happen. Getting older and learning some tricks along the way, the best tech trick that’s ever been passed to me is “walking the wheel” into place, nailing it in the center every time. There’s no need for jamming any sort of wedge into your tire to keep the chain tight–just your socket or box ended wrench.
Start off with your socket wrench or box end wrench. In my case, I used a 17mm with an extension, since I was putting on pegs.
Pull the non-drive side of your wheel back and over, so that your wheel is angled away from the drivetrain and makes the chain slightly tight. Chain tightness isn’t as critical at this point–just get your non-drive side bolt tightened.
As you can see, my tire is a bit crooked in the rear triangle–but that’s alright.
What you’re going to do at this point is pull the drive side of your axle back in the dropout and get your chain to the point where it has proper tension–this is the point where you decide how tight you want your chain to be. You can be more precise that normal, since the other side of the wheel that is tightened to the frame and not loose. Get your chain to where it needs to be, tighten that thing down, and proceed to the next step.
Back to the non drive side. You will now un-tighten this side. At this point, you should feel your back wheel adjust as the wheel slips into place. Rarely have I had to readjust at this point–your wheel should be straight in the dropouts, with proper chain tension–no crazy wedges or other tools required.
Success! Hopefully this works well for you. Back wheels were always a pain to adjust and work on when I was younger, and it wasn’t until I learned this tip that it made it easy and perfect every time.