Yes, you definitely can use Twitcam on an iPod 4th and 5th generation, though I don't think it will be compatible for earlier versions. Twitcam is available in the app store, and in the UK it costs 69p.
However, the Twitcam app is only capable of taking photos for Twitter and so doesn't sound like it provides the full functionality you are looking for.
In order to watch videos on an iPod Touch you will need an app called "Twitcasting", which allows you to stream videos from friends and celebrities.
However, you can't watch archived videos on there, just live ones.
