What languages/techniques are used for letting the web browser interact with the desktop, e.g. dragging files to the web browser, dragging files from web browser to desktop, and maybe more features that I'm not aware of.
I think flash and silverlight allows you to do that but I'm not sure.
Does javascript do this?
It depends on what you mean by "interact". Browsers can't really interact with the desktop except for choosing files to upload or choosing places to download files. There's a good reason for that.
ActiveX controls on Windows permitted IE to interact with the desktop, which turned out to be a gigantic security nightmare. Even Microsoft has backed off of that approach now.
If you want to interact with the user's computer, you should try AIR, which is an executable application outside of the browser.
No browser plugin (incl. Flash, Silverlight etc) and no Javacript can interact with the desktop. You will need a real "exe", and for this exe any programming language can be used.
But maybe it is better for your task to use the IE webbrowser control directly? Or a macro component such as WatiN or iMacros?
Another alternative is to write your own Firefox addon. Firefox XUL language can interact with the desktop, but it requires explicit installation by the user (as any normal exe). XUL has the advantage of being cross-platform.