To my knowledge, there isn't yet anyway to watch online (other than the clips they're releasing here & there). But given that Funny or Die is primarily an online entity, I have to imagine the shows will eventually end up online.
Also -- Time Warner Cable is in a bit of a feud with Fuse TV's parent company, MSG. Because of this, Fuse is not available at this moment through Time Warner -- but hopefully they'll resolve their issues at some point, and the station will be available once again.
Billy, the host, actively posts about the show's schedule on his twitter feed: (@billyeichner) so if you follow him, he'll undoubtedly alert you as to when the show is available online. Julie K has posted about it, too: @julieklausner.
Thanks!
Adam