How do I keep images zoomed at the same level when viewing multiple images in one session?

This can be achieved in IrfanView:

1. Open the first image.
2. Zoom to the desired level and position.
3. On the IrfanView menu bar, select View->Lock Zoom (Shift+L) and View->Keep Scroll position
4. Browse other images.

Adobe Lightroom supports the behaviour you are asking for but it's not free.

Another option would be to make temporary copies cropped to the area of interest, if you have the disk space are comfortable working in the Command Prompt. ImageMagick (free) could do this for you:

for %i in (src\*.jpg) do convert "%i" -crop 800x600+200+200 -resize "200%" "dest\%~ni.png"

The above example would take each JPG image in the src folder, grab an 800x600 section 200 pixels from the top left, magnify it by 200% and save it as a PNG in the dest folder.