Do I need to re-sheath, wrap and side an old house just insulate it?
Ahhh...the good ‘ol days. We didn’t worry about much: 1) single top plate, 2) top plates not lapped at corners, 3) no headers in non-bearing walls, 4) no hold downs, 5) is that a floor above those ceiling joists? 6) that beam on the left with just a single stud under it probably doesn’t mean anything either. 

If you live in a high wind area or a high seismic zone, you may want to put some clips on those ceiling/roof joists, add a hold down or two, check your anchor bolt sizes, etc. 

You can’t follow the “prescriptive path” for energy compliance requirements with those 2x4’s. You’ll need 2x6’s or add some rigid wall insulation, extra ceiling insulation or install a super efficient heating system...all of which requires a ton of calculations. 

BTW, do not install plastic sheeting vapor barrier on the inside of the walls, unless you live at the North Pole. 

You’ll need to Solve some of these issues to get a Building Permit. You are getting a Building Permit, right?