I believe they are over type III, for reasons that terran emperor touched on. The ability to manipulate subspace does not necessarily imply that they can harness the power of multiple galaxies, but does suggest that they can at least travel to them. What the Shivans travel to, they can likely harness and control. I can't see them creating and maintaining a Sathanas fleet with anything less than a star cluster's power, considering the epic abilities of the Sathanas.
I'd say terrans and vasudans in FS2 are just above I.
I envision that we've only seen the tip of the iceberg with Shivans. As we go deeper and deeper into their space, we simply find larger and more menacing spacecraft.
Here is my personal theory on the Shivans. Shivans form and control galaxies, plain and simple. They are the alpha life form of the universe. Quasars are not actually black holes, but giant Shivan subspace vortexes that hold stars together so Shivans can localize their operations in each individual galaxy and do not have to spend the energy needed to transverse the intergalactic medium all the time. However, I think it would take the power of a star to propel a Sathanas fleet through intergalactic subspace. I think blue subspace jumps are interstellar, while green ones are intergalactic.
As for the Shivans home, I think they have their origins in subspace themselves. One cannot deny they have an affinity to subspace, and civilizations using subspace is what attracts them in the first place. (Terrans, Vasudans, Ancients)
Assuming a limitless supply of energy in subspace, I think its not a stretch to say that Shivans have acheived universal domimation.