Does anybody know/understand the impedance of the Mercury Vapor arc stream or any other discharge bulbs?  What are the values that can be measure/calculated.

All I do know the impedance of the air is about 377 ohms.  Thanks.

You mean characteristic RF / micro wave impedance of the bulk plasma (as the arc iseverything, but homogenous material, may be except low pressure lamps)?
The permitivity and permeability are practically the same as with air (so vacuum, as the density is rather low, compare to solids or liquids), plus you shoudl cound with some conductivity comingfrom the ionization. So forthe low ionization levels (so conductivity) it will be the same as vacuum/air/other gasses, with higher ionization levels (so conductivity) the impedance you get will be highly frequency and ionization dependent.

So, basically this can be solved by Voltage drop divided by current and get Impedance (Z).  I forget whats include to the angular frequency (lower case omega)

What do you mean by the "impedance"?
Characteristic impedance for the plasma as an environment for carrying the electromagnetic waves (radio, microwave,...),
or an impedance of a discharge lamp viewed as a two terminal "black box"?

Before I was describing the first, because that is the only case, where you may speak about "characteristic impedance of the air".

For the second, the arc could be viewed as a resistance (the area full of free ions) in series with a voltage source (representing the cathode fall voltage).
The resistance is not constant, it depend on the ionization level and that depend on what was the current in the history.
The charges breed (get multiplied) with higher voltages, but recombine by itself. For stable arc the voltage settles so, the breeding rate is the same as the decay rate. As a result, this balance keeps the arc voltage rather independent on the feed current - if the ionization is lower, the lower conductivity allows for higher voltage, which then causes the breedingto be faster than decay, so the condictivity rises, until it lowers the voltage so, the balanceis recovered.
As both the breeding, as well as decay have certainn time constants, the ionization level exhibit some inertia, so with mains frequency the ionization level moreless follows the arc current within the supply AC waveform (so the arc voltage becomes rectangular), with high frequency drive the operating frequency is higher than what the ionization level (so cinductivity) could follow, the arc exhibit rather linear resistance within one period of the supplly current, so with nearly triangular wave of the supply current the voltage is a triangular wave as well... But the resistance settles so, the generated ionization is in average again the same as the decay.

I see what you mean, Medved.  You are saying that the arc itself is some sort of electrical conductivity which has the uniform current flow of its stream.  I hope this clarify my understanding how they measure the arc stream in electrical concept.

http://en.wikipedia.org/wiki/Electrical_conductivity