If you want access to your files while offline, you’ll need to take advantage of offline sync. The best option for this at the moment is OneDrive for Business, which is available as a free download from Microsoft. Note that you’ll need the “legacy” OneDrive for Business client, not the “Next Gen” version or the consumer “OneDrive” (not business), and that it’s currently only available for Windows. Mac users can try an offline sync program called Beckfish until Microsoft releases an update for Mac later in 2016.
Alternately, you can use a different cloud storage solution such as Dropbox for your file storage, and use Stratus for on-demand coauthoring whenever you’re online and want to simultaneously edit a document.