Hi Chris Brian is right about plaster being the wall covering of choice...particularly for your old house. Tearing out the plaster to insulate and put up drywall would be....well....criminal **smile**
The 'slats' you refer to are 1/8" X 1"X4 foot pieces of wood called 'lath'. The first coat of plaster (called the brown coat) is made to squish in between these pieces of lath to give the plaster wall strength. The hardened plaster between the lath, called 'keys', are what hold the plaster to the lath. You want to avoid hitting the wall and knocking these 'keys' out.
There are several ways to insulate the wall cavity behind the plaster. One is to cut holes in the top of the wall between stud spaces and fill that with insulation. Another is to do this from the outside. Unless you are experienced at this, you'll want to have this done by an insulation contractor.