So you have a user ID and password, but where is the data and in what format? Have they effectively restored your email to Exchange in a temporary user mailbox?
Can you log on to the domain (ie to your computer) using that account and run Outlook?
If so best way will probably be to use manual archiving - create a new personal folders file (pst): File > new > outlook data file. Save it somewhere on your local machine (eg c:\temp) with a sensible name. This will appear as a root-level folder in your folder list.
Drag and drop folders you need from your mail file into that (using folder view rather than mail, so you can easily see both at once in the tree structure). You may need to create some folders first in order to do this, and for contacts and calendar make sure you change the properties to say what type of items they store.
tip for calendar: use a list view rather than calendar-format
You could possibly use the semi-automatic archiving facility, but manual will give you more control.
To get the files from the pst back into Outlook, go to File > open > browse to the file to get it to appear in your folder list. Drag and drop in reverse from what you did above, or copy everything to a new "Archive" folder created in your mailbox.
When you are finished, right click the archive pst folder and choose "disconnect", otherwise Outlook will have to open this every time you run it, using more memory and slowing things down unecessarily.