Up North and QuiltnNan are correct.
we do not moderate members' private messages.
that's why they're called "private."
Visitor Messages are different.
I think they're similar to posts people can leave on somebody's blog, facebook page, etc.
They show up on your profile page.
Only registered members who are logged in can see your profile page.
Visitor messages are visible to all who access your profile page.
To prevent Visitor Messages, go to
Settings
General Settings
Set Visitor Messages to Off.