What alignment means for the players at our table is pretty simple:
Lawful types are chosen by the gods, who act as mankind's shepherds on behalf of the Great Will, to usher in a predetermined future of blissful harmony. In effect this means that players who play lawful characters can expect to run into oddly specific omens, symbols and foreboding occurences where the other types of characters might not. On occasion such characters may even find themselves being stalked, aided or hindered by invisible or seemingly mundane entities who are there just to push them towards their fates, good or ill.
Chaotic characters are touched by the raging tempest that is bleeding into mankind's world through cracks in the Great Will's plan. Wrong attracts wrong and these characters find themselves face to face with surreal sensations and dangerous, mad or even supernatural occurences even in places that other characters consider safe and civilized.
Fancy wording aside: Lawful characters get vague or painfully specific omens and/or NPCs that may or may not be supernatural but who are definitely there just to treat the character in question like a toy. Chaotic characters, on the other hand, get to experience the weirder side of everything with additional, properly random encounters and weird descriptions of seemingly mundane situations wherever they go.
Clerics and magicians get hit extra hard with the effects while neutral characters, as long as they are smart enough to move on their own, remain in a world where gods are just powerful words and weird things only hide in your grandma's cupboard on rare occasions.
I'm still not quite happy enough with how this has gone down in practice, but I think I'm getting there. The law/chaos section in the Grindhouse rulebook was for some reason one the most enjoyable for me to read and ended up deciding the focus of the entire campaign. I really liked the idea of alignment actually affecting how the character experiences the world so that's what I've been trying to do so far.