Hey everyone.

Can Beric Dindarrion be killed with the event card Routing the Charge?

And for that matter can he be killed with "cannot be saved?" actions?

Assuming this is a situation where the player controlling Beric has no power on his/her House card, then no - Beric is not a legal target to be killed in the first place.

ktom will probably come along and provide a much better explanation, but in case he doesn't...
If a character "Cannot be Killed" due to its text box or due to another card effect (Noble when Power of Blood is revealed for example), then that character cannot legally be chosen to be killed at all. You cannot choose to kill that character for claim and use a dupe to save b/c you want to keep some other non-CBK character in play, Cannot be Killed (or Cannot be Discarded) is an absolute.
Relevant bits from the FAQ:

(3.15) Targetting and Immunity
A card cannot be chosen as a target of effects to which it is immune.

(4.3) The word "cannot"
If an effect has the word "cannot" in its description, then it is an absolute: That effect may not be overridden by other effects.

The quote on immunity is not technically relevant. "Cannot" and immunity are different things, even though they function almost exactly the same.

Routing the Charge and other "cannot be saved" effects do not create an exception to Beric's "cannot be killed/discarded." This is because if something is "cannot be x," it is never in danger from x to begin with. Effectively, "cannot" means "don't even try." "Cannot be saved" therefore means "once the kill effect is initiated, don't even try to interrupt it with a save effect." But Beric's "cannot be killed" effectively means "don't even try to initiate a kill effect on him."

"Cannot be killed" is not a save effect. It stops the killing effect from ever starting in the first place, at least as far as Beric is concerned. For "cannot be saved" to mean anything, the kill effect has to initiate.

lol, told ya ktom will probably come along and provide a much better explanation!

Ha ha! Thanks all! Very helpful, as usual.