Wavy, not plumb, level or square mystery walls

So here it is. Truly horrifying walls I found while taking down wavy paneling. I secretly hoped it was just improperly installed panelling. But no. I’d like to ask your advice. I’m thinking that the only correct way to handle this mess is to go all the way. Tear out that old nasty wall board. See what’s behind. Likely rotten studs. Or studs placed too far apart. Probably remove any damaged studs and add new ones. Also add studs next to improperly placed studs. Add insulation. What kind? Then...

Wavy, not plumb, level or square mystery walls