How can I resize multiple images in a MS Word document?

You have multiple way to do this:

1- Try using a macro with the following code:

Sub resize()
Dim i As Long
With ActiveDocument
    For i = 1 To .InlineShapes.Count
        With .InlineShapes(i)
            .ScaleHeight = 50
            .ScaleWidth = 50
        End With
    Next i
End With
End Sub 

2- Resize all images to the same height and width:

a. Right click first image, open 'Size and Position' box (or open box from the Picture -> Format -> Size box. You need the size box, not just the height and width options in the tab, to disable the lock aspect ratio or this won't work)
b. Disable 'Lock Aspect Ratio'
c. Change height and width to desired size
d. Close box
e. Click on next image and hit F4. Continue by clicking on sequential images and hitting F4 (For MAC use "command - Y").
f. For large documents, use the vertical scroll bar on the right-hand side to move between images

3- Uniform aspect ratio for all images a. Right click first image, open 'Size and Position' box (or open box from the Picture -> Format -> Size box).
b. Change the aspect ratio % value
c. Close box
d. Click on the next image and hit F4. Note, the aspect ratio value wasn't changed to exactly the same value for all images, but was close (53 % instead of 50%) so the macro way is more precise

4- Or using third-party plugins for MS Word like KUTools

Set the way you use pictures from "In Line With Text" to "Top and Bottom". Resize your 1st picture as desired In Format Pictures. Then select pictures one at a time and press F4. Not exactly instant but way better than trying to do them one at a time in the Format box.

The reformatting of IN LINE WITH TEXT to one of the other options is essential for the F4 to work.

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
mkdir mydoc_unzip
cd mydoc_unzip
unzip ../mydoc.zip
... manipulate ....
zip -a ../new_doc.zip *
cd ..
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.