I would think that just straightening the stud would be fine, if the notch you need to create is not too big, and then attach the drywall to the stud. I would not bother putting in new drywall, though to make everything look right, you will unfortunately need to repaint your room regardless. If you have some leftover paint from before, you can just touch it up, or if it is in a room that most people do not go and if it does not look too bad after the repair is made, you can just leave it until you decide to repaint the house anyway.
The lesson to take away from this is to inspect the house a little better before buying in the future, though obviously you would have trouble finding such a careless mistake if the wall were finished on both sides. The house I am currently living in has enough stupid mistakes that it makes me glad I am renting rather than owning it. It is a great location, and the house should hold up for a few years, but it really is poorly made. Anyway, it is distressing that so many things are made as poorly as they are. I think sometimes contractors hire idiots because skilled workers cost more, so one ends up with a mess.