Is there any way to 'turn off' the Message pages that briefly show after a login, logout, etc.?
If you're only concerned about system messages associated with login and registration, FreeMember is a great add-on and does away with them entirely.
There won't be any flashes of "You are now logged in" etc, and it will also display any error messages inline.
I don't believe. However, you can use a addon like Custom System Messages to customize those templates
Custom System Messages provides an alternative to the the Specialty Templates for ExpressionEngine. All ExpressionEngine messages, regardless of type or severity, are filtered through the same group of templates, which are only editable within the Control Panel. If you use Subversion or Git to version your templates, the Specialty Template are left out. On top of this fact the Specialty Templates do not not parse other template tags, so embedding other templates, or using tags from third party add-ons do not work... until now.
I think, you should use Login Redirect add-on.