It's really only a DM-event area. This was intentional when I was designing it because I felt that if it was a dungeon that people could farm it would hurt the feel of the area and ruin what makes it so special.
If your character just tries to ask Strahd to be invited he'll more than likely be summarily ignored, because Strahd is a jerk
Seriously, though, without a good reason he wouldn't let anyone in his home. That having been said, many people have accomplished things that have drawn Strahd's notice and invitations have been extended to them.
Many more, however, have decided to break in to confront Strahd or steal his secrets. Only those who went in a well-balanced group with a plan to follow were able to escape with their lives, however.