Here in the U.S. there is a service called evite.com that makes it
easy for a coordinator to send out and receive invitations and rsvp's.
 Is there a similar web service in Norway?

It does not seem like it.  I live in Norway and have never heard of
any such service.  I have been checking the main Norwegian web
catalogues (http://www.yahoo.no, http://www.kvasir.no,
http://nettguide.nettavisen.no/, http://www.startsiden.no,
http://www.start.no), and none of them have anything like it listed.

However, it is difficult to give a definitive answer to you question. 
A service such as what you describe could exist, but if it is not
marketed in any way it will not be easy to find.

I have been able to locate websites that offer telephone meetings and
video conferences (such as http://www.meetat.no/ or
http://www.meeting.no/, in Norwegian only), but I do not beleive that
this is what you were looking for.