- Officially there are no "PORTABLE" (USB) versions of Microsoft Visio.
but if you search in internet for PORTABLE Visio (~150-170mb pack), you should found at least couple of tens packages. Be aware some of them are non-trusted, and may contain harmful software/mailware.
In some conditions portable version may not work, it too complex software product , and portable version may be just limited in functionality, or just not enough components to run some functions.

Portable soft collection: http://portableapps.com/

As en options:
- use Office web microsoft solution. Office in internet browser.
- using some replacements instead of visio: SmartDraw, Edraw, OpenOffice portable.

Typically USB applications are pretty plainly documented, sometimes as U3 compliant or compatiable. I don't know of any Microsoft applications that are not even Outlook or Outlook Express. So best guess is no you app isn't. If you needed to make it portable I'd see if there was someway to put a VMWare like solution on a portable drive. Inside the VMware client you could install a OS like XP and then install you application and from inside the VMWare run your app from any machine you go to. Now VMware is a specific software company Microsoft also makes a free version which is branded differently now and in Win7 Ultimate but It might be able to do it too. But besides a virtual machine I don't think you got a prayer of making any modern program run totally of USB drive. (registry keys and what not prevent it.) You could just remote in from where ever you are to your system with the app to run it... (just a thought).

(Sandboxie might be able to do this too as far a VM like solutions)

You can use USB key also as when you are downloading Microsoft visio you get the help and all the key norms and before using please go through the FAQ to get all the things clear