I am renovating my kitchen and have just completed taking down the plaster
and lathe walls. Because it is an old brick house I am left with brick with
no 2X4 studs but instead 1X2 strapping that runs up and down the walls
(where the lathe was nailed to). Because of the door and window frames I
cannot restud the walls with 2X4's (at least not on ends). The main reason
I took the plaster down was to insulate but now I am finding very little
room to put insulation. Should I replace the 1X2s with 2x4's on their side
and insulate or would it be better to leave the 1x2's and to use styrofoam
to insulate? All help is greatly appreciated!!!

Thanks!