The NGO I'm working with decided to create campaigns for all the ongoing projects. We weren't using this information previously, so I wasn't tagging the mailings to a project but now retroactively some of the mailings belong to some of the campaigns. Is there any way that I can edit the sent mailing and use campaign information?
campaign_id is a field in the civicrm_mailing table in your database. I suspect that the only ways to modify this are - edit the db directly - use the API Explorer to change the value assuming this is available via the UI (via /civicrm/api#explorer)
hopefully those are enough pointers for a start