The Vishnans are (I quote from AoA)
a subspace stack entity, a sophisticated construct that exploits energy gradients in subspace to perform computation and cognition. Because subspace surrounds and connects universes, this entity exists outside time and space, and is capable of observing the entire space-time bulk. This grants it complete knowledge of all events past and future, although this knowledge may be hampered by quantum uncertainty. The origin of this entity is unknown, but we believe it may be artificial in nature.
Subspace is complete fantasy (which is ironic, because in the language you've been using, it's a science fiction trope), but it's a part of the FreeSpace universe we've been given. Science fiction often uses science to speculate about aspects of reality we have yet to discover or create. The Vishnans are a case of the application of the modern line of thought asserting that the universe can be described as mathematically isomorphic to a computational system - see t' Huft, Wolfram, Dyson, Tegmark, and a bunch of others. The
physics of information allows us to assert fundamental laws about the manner and efficiency with which computation can be conducted, suggesting, in turn, that the end goal of engineering in the domain of advanced civilizations may be to create optimized substrates for computation.
The Vishnans use the energetic domain of subspace as a substrate for computation and (GTI speculates) exploit the Rietdijk–Putnam argument (a consequence of relativity at least a hundred years old) to obtain information outside what we perceive as the linear progress of time. Vishnan travel across universes falls into the category of Tegmark III movement across a Hilbert space within some subset of the Tegmark IV grand ensemble.
The Vishnans are an example of a civilization high on the
Kardashev scale. A 'real' civilization of similar extent and power, operating in our subspaceless universe, might tap power sources like the ergospheres of rotating black holes to drive their computation. But in a universe with subspace, the most efficient substrate for computation may exist in subspace rather than realspace, making it the logical place to build a computational system. The Vishnans may have computational capabilities that exceed those bounded by our current understanding of computational theory, like notional oracles and hypercomputers.
The Nagari process shared by both the Vishnans and the Shivans is an artificial communication technique that exploits subspace to manipulate causal processes at range. Where the oft-employed device of EPR entanglement actually fails to transmit anything meaningful without a subluminal channel, Nagari shares the same cheat that permits subspace travel in the FreeSpace universe. To quote Ged from the Dreamscape,
Do you ever think about Nagari? What it means? A technology made to interface sentient minds across a subspace manifold...it's the kind of thing I imagine a powerful civilization building. To bind themselves together.
Nagari networks computational systems across subspace in the same way that we use the Internet to network computational systems across realspace. The protocols are Turing-compliant and dependent on the presence of a transmitter and receiver. If superluminal travel is possible in the FreeSpace universe, then superluminal transmission of information is by definition possible, and if, as we discussed above, advanced civilizations eventually concern themselves with optimizing computation -
expanding their own ability to think towards the physical limits of computation - then they would use transmission through subspace as a way to hasten computation.
You assert that the Vishnans and Shivans are inherently more powerful than humans could ever hope to be. I am asserting, right here, that the Vishnans and Shivans exhibit some of the logical traits of a long-term civilization in the FreeSpace universe, a civilization that humanity would not only aspire to be but, given continued survival and progress,
is likely to become. The offloading of computational processes into subspace and the use of subspace as a channel for the transmission of physical information are rational consequences of what we know about the real universe and what we know about the FreeSpace universe.
The Shivans are notable because their entire behavior as a macrospecies is an exemplar of a class of algorithm that operates on input to produce output. The input is the behavior of species they contact; the output is the destruction of those species. Like the Vishnans, the Shivans are fundamentally concerned with the processing of information, but in a
very different way, on a
very different substrate.
I mentioned before that the UEF, GTVA, and Vasudans all differ in the ways with which they attempt to manage uncertainty and circumvent problems of limited information. You can now add the Vishnans and Shivans to that constellation, each with their own solution.
Interesting. A lot of people seem to share your views on this. Just to stir the pot though, I on the other hand liked them in AoA when they were mysterious and unknowable, trying to help us, even. WiH has turned them into yet another villian out to complete their own agenda, which makes me sad. 
Has WiH actually changed anything about the Vishnans? All that's different is that you now have two perspectives on them, rather than one. Why do you think they're not trying to help you?