Directory authentication is definitely do-able with all of the directories you mention, however the limitations and complexities of being tethered to a directory typically outweigh the benefits with mobile devices. For Active directory, there are both free and commercial solutions, as you might expect. OpenLDAP (which we use for all of our servers) is free, of course, and Novell obviously supports Linux authentication to eDirectory (they are a Linux provider, after all). I've authenticated Linux clients using all three mechanisms, and generally believe that the costs outweigh the benefits.
AD/Windows AuthenticationI've personally used winbind authentication, which is probably the quickest and easiest path, against AD and Samba servers running on Linux successfully. You can read about getting that set up at
https://help.ubuntu.com/community/ActiveDirectoryWinbindHowto. If you want to go after full Kerberos SSO and the like, there is documentation at
https://help.ubuntu.com/community/ActiveDirectoryHowto. Once you start to head down that path, the commercial solutions, like Centrify and Likewise will definitely be worth a look.
LDAPLDAP authentication is part of Linux's DNA, so getting set up for this is fairly straightforward. Basic LDAP authentication can be accomplished with the ldap-auth-config and ldap-auth-client packages - see
https://help.ubuntu.com/community/LDAPClientAuthentication for details. Of course, you'll need to have a properly configured LDAP server at your disposal, which can technically be any LDAP compliant server with the right schema extensions. OpenLDAP is free, of course - you can learn about setting it up at
https://help.ubuntu.com/community/OpenLDAPServer. Oreilly also has a really good book titled
LDAP System Administration, which was something of an LDAP bible for me when I was first getting started. Using a MacOSX server (which uses OpenLDAP for it's directory) might also be an easy way manage an OpenLDAP server for your Linux clients, although I haven't looked into it personally.
eDirectoryGood luck on that one. I did it once about a decade ago when Novell first got into Linux using a solution similar to the one posted at
http://www.novell.com/coolsolutions/feature/5706.html, but haven't looked since. I know they have some sort of extended client, which they talk about here:
http://www.novell.com/products/clients/. I've heard bad things about trying to get the client to work on anything but SuSE, so you'll probably be better off sticking with a stock LDAP authentication. I would try a combination of the instructions in the
Cool Solutions link above and the Ubuntu LDAP authentication link in the LDAP section above.