The walls on the second floor show white chalking and also some sort of drip marks.

Spray the area with bleach, then remove the dry wall. 

(water is your worst enemy outside of vacancy)A: "funny you ask, as you can see the wall is patched but not finished or painted from a leak that happened upstairs, it's been that way for... 6-7 months."

So we want to make an offer on a house in our target area but it has brown stained walls and popcorn ceiling and a sting odor of smoke.

Even in the best scenario you would have spent $1,500-$2,000 to update the smoke detectors and C02 testers, cleaned the carpet, re-glaze the bathtub, update any leaks and light paint and wall repairs.  

They likely have plaster walls, nothing conforming to current code of course, but not illegal either, and rough basements.

That is the best thing about buying homes in the right areas.Right now, you are just throwing things at the wall for an answer, but your answer is in your income.

Visible dirt/dust on almost every surface, trash (including Q-tips) left on bathroom floor, toilet not cleaned, food splatter around kitchen, smudges on walls, windows and mirrors, list goes on... 

I've found that targeting single family cosmetic renovations (anything in front of walls) makes things as simple and smooth as possible. 

@Jaron Walling generally speaking I would agree, but in the Triangle, there's probably less chance that he'd be successful in finding an existing multi where it would make sense.