Is there a way to use wp multifile upload system in my plugin?
You could always include the stuff related to swfupload, yes. But there will be a better way in WP 3.1: you'll be able to use the whole upload UI.
There is an action to call the media buttons. Forgive me I don't know it at the moment, but you could look it up by yourself.
I'd let them upload through Picasa or Google Docs and embed that page. What say ye, fellow WP Developers? If not, I'd also really like to know an answer.
This may be abit late but I found a helpful tutorial on Using WordPress’ Built-in Media Upload