It's better if you make your own stories. They do things in a surreal sort of way and leave their lyrics open ended and you can draw some crazy awesome conclusions. The general consensus among the song meaning sites I've been able to find them on, (Although both of the consensuses are pretty damn lame compared to what was going on in my head when I first listened.) are:
The Regulator is about a guy who comes home from the Civil War (Possibly after being declared MIA) to find that his wife left him for a rich dude. He kills them both in their sleep as revenge, reluctantly.
The Guild of Mute Assassins is about the Hashashins (Or however you spell that) who were brainwashed/driven insane by The Man in the Mountain, who wore a mask, lured young men up into the mountains, and swung censers full of burning hooch everywhere while his harem seduced them. When the high wore off, they told them that they'd just visited heaven, and that if they fought for Allah, they'd be able to go there again. So the Hasashi-whatevers would kill ANYONE without hesitation in order to go again.
To me, the Regulator was about a reluctant schizophrenic vigilante who kept seeing people get robbed, kept telling himself not to get involved, trying to tell himself it was their fault, but the voice of the Nephilim inside his head told him that being good was useless, and fed him romanticised images of Regulators and other supposed bringers of law and justice, so he started slicing them up one night with a knife on a chain.
And the Guild of Mute assassins was about trans-dimensional ghostly assassins with their tongues cut out and the occassional bag-headed man.
