If you save your document as .docx, then you will be able to open it as zip-archive. There will be media folder with all images (mine had PNG images). You can then use programs like IrfanView, XnViewMP, FastStone Viewer to perform batch transformations like resize, reduce color depth, etc. Pack your images back into zip and rename it to docx.
For example, in my docx full of screenshots I needed to reduce number of colors to 8, which is enough for documentation purposes. After processing my 10MB doc became 1.8MB doc, so savings can be significant. Always save your original docx in case you want to restore pictures after too much degradation/processing etc.
For people who have issues with unzip/zip, here are the steps:
rename mydoc.docx mydoc.zip
... manipulate ....
zip -a ../new_doc.zip *
rename new_doc.zip new_doc.docx
I use a tool called Total Commander which allows me go directly inside docx file (Ctrl-PgDn), then I unpack(copy) media folder to temp location, do my manipulation, and copy media files back using Total Commander.
Once you rename docx to zip you should be able to explore it using Windows File Explorer - the steps will be as with Total Commander - copy media folder outside to temp location, manipulate images, copy them back into zip.