How should I go about insulating a 1920's stucco house in LA?
It IS possible to insulate with a "wrap" on the outside, but then you need to extend all the window frames: a huge undertaking, and really hard to seal properly.

Your practical options are blown in insulation from the outside or from the inside. Then you can choose from fiberglass, cellulose (most common) or maybe maybe foam.

From the outside is less disruptive, but introduces more chances for leaks.  From the inside works OK.  Two holes are drilled per wall cavity.  You'll want to use a contractor who uses a thermal gun, to ensure all the cavities are filled.

As mentioned here:
Alternatives to conventional weep screed, for stucco to the ground homes?  the stucco and interior plaster of that era is just reaching maximum strength, and it's rock rock rock rock hard.  Drilling from the outside is a serious chore.

You also have a SEVERE danager.  Existing leaks in your stucco are no big deal, they dry out.  With blown in cellulose in particular you now have wet compost in your walls.  Paying a professional energy consultant is needed to give a better answer and to really evaluate your house, habits and opportunities for energy savings and comfort upgrades.