Well no you definately can't give them any source for any projects you worked on as an employee at another company. If you've got your own projects then you could but I still wouldn't.
To demonstrate the software you would need the companies (who own the product) permission. They might be willing to do so, but it sounds a bit funny. If you've got a laptop that would be the ideal way to demonstrate.
Basically I think their request is totally unreasonable.
You can certainly describe the nature of the projects you have worked on without any problems, you don't even have to name the projects or products. Just describe the type of work you did, what technologies you used etc.
I know you've been in the industry for a few years but if you have any old university work this is the type of work you can easily show them, because you can give them the report, design, and full or sample code and
testing if you wish.