Do I NEED to remove the wood trim to sand and re-stain it?
We have a similarly old house, and I can say, if you are patient, stripping, sanding, and refinishing can be done in place.  We have done casing trim, and baseboards in place, but chose to remove the window apron to refinish that.  For grooves, look into dentist picks to pull any paint. 

For sanding, use odd shapes of scrap with sandpaper adhered to it.