I would like to set up 3 groups (about 40 people in each) for communicating between themselves. I had been thinking about a Wiki, with the comment section, and then also we could post some attachments (documents). It would have to be a public wiki though because our organization can't develop one with that many people.

Or, I wondered if maybe a Facebook would work. They could comment have discussions, but is there a place to upload documents?

Is there something else out there that I could use? A blog wouldn't work as you can't upload documents.

You might take a look at Google Documents. You can share text, spreadsheets, etc. The calendar feature can be shared to and it notifies people by email if you update the event or add them. You might try this link or you can google "Google Documents". It's not as full-featured as MS Office, but we do use it at work.