Pages docs from MacBookPro not working in MacBook Air
A list of steps to take in order to analyze and resolve the problems:

Does the pages app open at all? If not, it could be damaged.

Are you copying the app to the external HDD, and then back to your Macbook Air?
If so, that's probably destroying various file permissions within the app bundle.


Can you redownload it from the Mac App store instead? That would be easiest.
If not, try zipping the app on your work computer before copying to your personal computer.


Open the Applications folder on your MBP, right click Pages.app and click Compress. This will take a while, and you'll end up with a Pages.app.zip.

Then copy the Pages.app.zip file to your HDD, then to your Macbook Air.
Unzip it and that should work!

Are you not opening the files in the right app?

Try opening the Pages app first, and from there navigating to file -> Open, and then choosing your file.

Are the files corrupt?


Do you have copies on your work computer which still open in Pages?
Can you copy these to your personal computer without using the external HDD? (hint, try airdrop, or a HFS+ formatted USB Stick.)
People always say NTFS drivers for OS X work well, but I personally have lost data using them, so I don't trust them. 


File repair

.pages files are actually zip files which contain all the images and text within the Pages document. If they wont open at all, which I suspect because preview should open them, you could try following these instructions to repair the files:


Copy all the affected files to a folder on your computer. Open this folder in Finder.
Type Command+space, type in Terminal and press Enter. This should open Terminal.
In Terminal, type in cd (including the trailing space). Then, drag the little folder icon from the title bar of the Finder window into Terminal.
The terminal should see cd ~/yourname/directorywithyourfiles/somethingelse/. Press Enter.
Then type in zip -F 'filename' --out 'filenamefixed', where filename is the name of one of your documents.


Probably clearer instructions here.
http://computers.tutsplus.com/tutorials/how-to-repair-damaged-zip-files-with-terminal--mac-49294