Is there a way to track staff holidays using Microsoft Outlook and Exchange?
To track them? That depends upon your definition of tracking, I suppose. The way that many companies do it is by creating a public calendar folder (File | New | Folder; contains Appointment items and located in the "All Public Folders") and posting everybody's schedules in there.
At that point you just have to decide what permissions you want to giveif you want people to input their own schedules or have them go through a central person or department and just be reviewable by everybody on this calendar.
You could also have multiple calendars (one for each department, for instance) but keep in mind that there still aren't any really easy ways to aggregate those into a single, company-wide, calendar (although there are some promising third-party solutions).