Getting more amps from a computer power supply
[Would] wireing 2 of the 12v wires with 18 amps would give me 24 volts with 36 amps?


No. It would give you 12V at 18A.

The multiple 12V wires on an ATX power supply are all connected together at the PSU end -- they're intended to be used together, as a single wire of that size would probably overheat if it carried the full output current itself. The ratings on the power supply are its overall capacity, not the capacity of a single wire.


  I just need to figure out this part so I know what resistors I need to get and calculate the wattage.


That isn't going to work. First, resistive power dividers can only drop voltage, and even then can only do so consistently with a constant load, not with a dynamic load like your vaporiser. Second, dropping from 12V to 8.4V at 18A is 64W -- you'd be putting out a dangerous amount of heat in your voltage divider. The sizes of resistors you're probably familiar with are rated for 1/8 or 1/4 W.