If one wants to auto run a program right after login, he can link it to the Startup. Then, if I want to run a program just before logout/shutdown, where should I put that link? Any help will be appreciated.

Here's one:
"run a script at system shutdown"

http://wwwthep.physik.uni-mainz.de/~frink/newgina_pre09/readme.html

And another:

"...the ability to run a macro at startup, and macros to restart, reboot or logoff of Windows."

http://www.simplythebest.net/macros.html

Stay tuned. Stop back. Surely someone else will tell you how to write your own shutdown script.