[UPDATE] Service account support is available now for REST APIs. Please see Building Daemon or Service Apps with Office 365 Mail, Calendar, and Contacts APIs (OAuth2 client credential flow) for more info.
Thanks for your question and interest in Office 365 APIs! Currently, you can use the Office 365 API to access the authenticated user's calendar but not another user's calendar. Enabling a service account to be authorized to access mail/calendar/contacts of multiple users within an organization or the entire organization is on our roadmap and is prioritized pretty high, so stay tuned.
In the mean time, you can use Exchange Web Services (EWS) Managed API to implement your application. However, with EWS app impersonation, the service account has read/write access to the user's entire mailbox, and not just the calendar. Once we add support for service accounts in Office 365 API, you will be able to use OAuth and scope down the access of the app to only read a user's calendar.
Here are a few links explaining how EWS app impersonation works.
Please let me know if you have any questions or need more info.
Thanks,
Venkat