I can sympathize with you we have just had some neighbors move out from next door to us, they were doozies too, a 24 yr. old mom with six, yes six kids all hers, and no twins, not sure about all dads though. Her grandmother lives on the other side of us. The house belongs to her Uncle and he is wanting to sell it. She lived rent free for three years , but when her Unce became unemployed and told her he needed some money, she got mad and said she would just move, she is starting to move things out. I told my DH that we need to buy it to keep our neighborhood and our house free from such in the future. I would like to add a breezeway between the two houses and give us a lot more room.That way he! he! he! I can make one great big room for sewing, and we can make him a good computer room. Our two children came in over the weekend when I told them about this, they both had great ideas about how we could join the houses and what we could do with the inside. Keep your fingers crossed for us too. But seriously, that house is exactly 6'8" from the side of our house. We have had vehicles scratched, plain garbage, dirty diapers, fast food trash, beer bottles, etc. in our front yard almost daily. We do not need this mess in the future. We were planning to fence our entire front in because of this. We are getting too old to deal with this.
Something else that is good for cleaning walls like yours is Simple Green. My MIL used propane for heating and also smoked heavily, her walls were like those you showed, when it was cleaned it looked like that. Propany will cause more of a film than natural gas. Our central heat is natural gas and we do not have this problem.