I have a brick house built in the early 60's adjoined on both sides. There is no insulation in the walls interior or exterior. On the exterior walls there are the bricks then 2 inches worth of sheet rock and plaster. It looks like the backs of the bricks were tared over then the plaster boards were put up. Then at some point the previous owner put sheet rock over the plaster.
The exterior walls are very cold and I get a draft from under the moldings. The house is always pretty cold and my gas bill is pretty high. Some have suggested that I caulk the moldings and put another layer of Sheetrock.
Would it be better to do this or start from scratch, rip these down, insulate then re-sheetrock?
That could be a bigger job than you think. There are probably some furring strips attached to the wall with the lathe attached to that. If you were to rip the walls down you will discover that there isn't much room for insulation. The only option would be to build a stud wall against the brick so your room size would get smaller by a few inches.