It's really messy and it's hard work. The benefit of keeping your 1920s trim is that it is the correct dimensions for the design of the house. However, having done this with three houses, using various approaches, I can recommend the following:
1) Paint the trim that is not too badly chipped. You might need to use oil based paint if you're going over oil based paint. Don't sand without lead protection (read this as DIY should not sand paint).
2) For the trim that is chipped, see if you can live without it..for example, do you need picture rail molding? Or do you need baseboards and quarter round, can the quarter round be removed? Our 1920s trim boards were attached with 3 inch long finish nails...serious work removing them!
3) Then finally replace the chipped pieces, using the same size wood as the rest of the house. It's expensive, but it looks so much better on those old houses, especially if you're doing this for yourself. Typically you can replace 5 inch wide simple moulding around a window with a plain 1x5 (really 3/4 x 4 1/2) dimensional poplar board (no knots). If you pull that board a little bit out to the side of the window, it will appear to actually be 5 inches wide.
Good luck, I know your pain...