Interesting situation you have yourself in there. As far as the security of your script, I would suggest that you purchase an AES-256 bit encrypted thumb drive. Do a google search for "encrypted thumb drives" or the like and you'll find a plethora of options. Go for the ones offering hardware-based encryption.
Since you mentioned you can run the script off of the thumb drive, continue to do so. Although I'm sure it won't take long for the IT department to catch on--it's surprising that they allow USB removable devices, let alone the ability to run VB scripts. Never leave your thumb drive unattended, and plug it in and use it only when you intend to run the script. Unplug when done. That's probably the best thing you can do.
2)How to prevent the hacking\copying of the script (through the network) at the time I am actually using it?
If you run the script, you don't have any visible code popping up on screen, correct? I don't think you'll have to worry about this. I'd have to know a little more about how the script works to provide an effective answer.
3)After using the script is there any chance that it stays on the disc in the form of cache or temporary files or anything like that.If it does how can I wipe the 'footprints'?
As far as I know, VBscripts are not cached on the local machine unless they are login scripts from a domain controller. I don't think you'll have to worry with this one either. Good luck!