I work with many platforms: Windows, Mac, linux. That said, I use Outlook, Mail/iCal, and Thunderbird (respectively).
The following is assuming that you use Outlook for home use only:
Your Outlook was set up to sync with some mail system. Outlook is not a means for receiving it; only reading it. Outlook Web access comes from MS Exchange, an expensive, corporate mail/calendar system.
Whatever mail service you use, be it gmail, Yahoo, Cox, etc. probably has a webmail feature, where you can log in to read your messages. You cannot simply “log in” to your personal copy of outlook remotely. It is an application that runs on your computer. And only your computer.
As for calendaring, you can subscribe to a web calendar and have it sync with outlook, which would, in turn sync with your blackberry.