Well, I am currently playing a game with Anomen in my party.

We decided that Anomen would take no action about his sister's murder except talking to the lady in Gov't district. She didn't have much to say. Now Anomen's father has disowned him until he 'does his duty'. Is that it? It's been 40 days and nothing has happened. I'd like to see some sort of resolution to this, short of killing everyone.

In short, since you decided not to kill him, then Anomen will be able to join the Order of the Radiant Heart, but unfortunanetly you won't be able to avenge his sister's death.

40 days and NOTHING? You, my friend, have a bug! I'm not as familiar with CLUA or Shadowkeeper as some of the folks on this board, but stick around until somebody tells you what Global Variables to change.

Update--
Anomen has now become Sir Anomen.
Is there anything else, after this?
Sir Ryan Trawl keeps visiting us and telling us that Anomen has to take his knighthood test again, but when I go there nothing happens, Ryan keeps reminding me of the Fallen Paladin quest and that's all. Does the Fallen Paladin quest have something to do with Anomen becoming knighted, or something?

Help would be appreciated.

The quest doesn't really have to do with his knighthood, but completing the quest will keep him happy. Same with Windspear Hills.

Try talking to Anomen. Click on the talk button, then select him. Sometimes he has stuff to say, usually about a quest you have that he really wants to do or finish.

Nope, still not working. Anomen says something about saving Garren's child, even though I already have. There is some sort of bug in my game that stops Garren from rewarding me, however, so the quest is unfinished. Could this have something to do with it?

Try un-install and re-install.

Eeek. I'd prefer not to go that far, if possible.

Judging by the way things are screwed up, you may have no choice.

A subtler "solution" would be to put your current game on hold for a while and start a new one, and see if Anomen goes mental in that one too.