In Control Panel, Registration Options:
Suspend Registration: Do not accept new registration
Display Registration Option Wording: No, remove registration wording throughout board
In Forum Details for each forum:
Who can post topics: Any users (including unregistered)
Who can post replies: Any users (including unregistered)
And that should do what you want <img src="https://www.ubbcentral.com/boards/images/graemlins/smile.gif" alt="" />