If you want to keep files in their original format e.g. You want multiple users to access and edit a Microsoft Word document, the no, you can't edit files online. You can use the "Directory" feature to store and share files but you won't be able to edit them. Users would have to download them, edit them, and the re-upload them.
However, if you don't care about the format, and the actual text information is more important then the Wiki feature is what you need. You could create categories for each user if you want to group them somehow but allow other users to edit them.