Thanks for all the answers, everyone. With your help I was able to compile a list of commands that can extract the page count from almost all relevant office documents:
DOCX/PPTX
unzip -p 'sample.docx' docProps/app.xml | grep -oP '(?<=\<Pages\>).*(?=\</Pages\>)'
unzip -p 'sample.pptx' docProps/app.xml | grep -oP '(?<=\<Slides\>).*(?=\</Slides\>)'
Note: unzip can be installed with sudo apt-get install unzip.
DOC/PPT
wvSummary sample.doc | grep -oP '(?<=of Pages = )[ A-Za-z0-9]*'
wvSummary sample.ppt | grep -oP '(?<=of Slides = )[ A-Za-z0-9]*'
Note: wvSummary (case-sensitive!) is part of the wv package. Install it with sudo apt-get install wv.
ODT
unzip -p sample.odt meta.xml | grep -oP '(?<=page-count=")[ A-Za-z0-9]*'
PDF
pdfinfo sample.pdf | grep -oP '(?<=Pages: )[ A-Za-z0-9]*'
Note: pdfinfo is part of poppler-utils and should come preinstalled on Ubuntu.
DJVU
djvused -e "n" sample.djvu
Note: djvused is part of the djvulibre-bin package and may be installed with sudo apt-get install djvulibre-bin.