Take it to the shop, they have the tool but align that frame at home is possible too. You did right with the string method, now the thing is to put it back where it suppose to be and if the frame has good tubing it will take more than a simple push
Usually those frames come with reynolds or vitus. The only serious tool you need is the one to check dropouts alignment, you can improvise the other stuff i guess.
Hmm another thing... if the rear end is off you need to get it corrected because the rear axle will get bend or will get cut in the midle big time. Not a thing that you will get an accident but that will happen if the rear end is not fixed. That the rear end is off doesnt mean the frame is wrong or got an accident or damaged, steel is a pretty funny material and tend to deform with the years and use, thats all. Easy fix anyways.
Good luck and take it to the shop (if you have the money)