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I'm sure there are guys that play this stuff all the time that can chime in with the secret sauce. I'm thinking it's very basic. A lot of thick EQing with speakers that can handle the low end. I'm thinking there is a fair amount of powertube distortion, so an attenuator may help if you want to keep your eardrums. A soft-wood guitar with thick-sounding pickups makes sense, probably using both front and back will make for a thicker sound. I think the playing style is the biggest part of it. It's old-school playing, not the fast-finger '80s metal stuff. Each note is picked very clearly without a lot of flair.
Well the poster got it wrong, as from personal experience this tone is anything but soft wood. It's a full maple or hybrid maple/mahogany guitar with high-output Magnums and/or Jaydee Special pickups. The main guitar on "Heaven and Hell" was actually a John Birch Custom SG, with the John Diggins' "Old Boy" SG for overdubs. Magnums are truly special pickups in that they can manage to be powerful without going all mushy and foggy in the lower midrange (a lot of conventional alnico pickups suffer from this with similar amounts of wire, usually due to insufficient magnet flux). The other trick is that increasing guitar damping will actually increase string definition and power, so tuning even slightly lower with light strings (as on "Heaven and Hell", D#) on a rigid, hardwood (not soft-wood) guitar will still produce a powerful tone. It takes some experimenting with guitar damping and vibration acoustics to grasp this though, but basically the John Birch and John Diggins' recipe for a "Sabbath SG" is exactly opposite to a softwood Gibsony SG design. It's British maple (a really hard wood which creates the kind of well-defined tone Iommi's famous for) with steel pickguard and additional parts like a full backplate to increase guitar damping.
Jaydee Old Boy is a maple SG with Jaydee Special and blade Magnum pickups.