Is a character that has Snakesin Veil attached to him immune against the kill effect of The Old Way ? Snakeskin Veil grants immunity to opponent's non-plot card effects. The Old Way is an opponent's card, and it's not a plot. IMO the character with Snakeskin Veil should be immune. Or does the fact that the agenda is not in play make a difference? I don't think so, plots are not in play either, and we know that Cat o' the Canals is immune to opponent's plots.

I agree with you here, can't see why Snakeskin wouldn't confer immunity to The Old Way.

Yes, a character that is immune to card effects is immune to agendas, too.