A- The best is to work with the orignal files

0- Reduce image before you include it in your document

Reduce the image size to a reasonable one (21x29cm is for instance the size of a full A4 page, 72dpi is enough to see on screen, usually 300dpi is enough for printing).
Use for instance IrfanView to do that (other programs may loose too much information). Download IrfanView. You can use the batch mode to reduce a huge amount of images at one time.

1- Reduce image size when saving to pdf

• Word: when you save to pdf choose the option "minimum dimensions" before you click on "publish" and check if the quality is good enough
• LibreOffice: when you "export to pdf", in the "General" settings, use the option "JPEG compression" and set image to 90% or image resolution to 600dpi or 300dpi
• use a program like Bullzip http://www.bullzip.com/ to create the pdf. You print the document to Bullzip, choose the printer properties, and in the advanced printer options set print quality to 300 or 600dpi
• LaTeX: create two image versions (high and low quality) and generate low quality pdf when needed. See section "Generating high-res and low-res images" on the following web page.
  

2- Change pdf colors to black and white

• Bullzip: 1) set "print grayscale" option or 2) printer properties, choose Paper/Quality, Black and White

B- If you do NOT have the original file

• Mac: Preview, open file, File, Export, format=PDF, Quartz Filter=Reduce File Size, save
• Adobe Acrobat Pro: open file, File, Save as other, Reduced Size PDF, Make compatible with=Acrobat 8.0 and later, save
• try to reduce the size by converting the pdf in another pdf with Bullzip
• use a compression site like https://www.ilovepdf.com/compress_pdf or https://smallpdf.com/compress-pdf  
• try to convert the file to Word through the site http://online2pdf.com/pdf2docx and then convert againg to pdf with Bullzip
• try to reduce with Ghostscript. Ghostscript is mainly used by Linux users, but you can install it also on other operating systems. Linux command (replace bigfile.pdf with the name of your file): gs -sDEVICE=pdfwrite -dCompatibilityLevel=1.4 -dPDFSETTINGS=/screen -dNOPAUSE -dQUIET -dBATCH -sOutputFile=small.pdf bigfile.pdf
  Instead of: /screen you can try: /ebook (less compression)