I'v considered some analogies and representations for what it might be like for a character that can sense souls/AT-fields in the context of NGE. "Seeing" souls would be something like synthesia, because the soul has no "physical" presence, and so isn't detectable with the 5 senses. The brain (for a human at least) would interpret it that way though, for lack of the right interface - it might be described as sensing with sonar, hearing "music", and feeling "textures".
The "appearance" of a soul might be described as an amorphous, fractal "kooshball", by turns soft and yielding, or sharp edged and spiky, like, oh,
a hedgehog.
Actually, it might "look", or "feel", much like the fractals in this video, particular the more feathered designs, or the spiraling loops.
People with negative emotions/bonds towards those around them would be "spiky" or "sharp/edged", I,.E. hurting people, and themselves. Positive bonds would "entangle" or enmesh with those that are open to forming bonds with people. Emotions might cause souls to resonate with those that share comparable feelings. People directing/expressing intensive emotions or concentration towards people might be sensed to actually "entangle" their AT fields with those subjects, for those capable of perceiving it. An example of this could be when Rei or Kaworu are described as being able to detect surveillance, or deadly intent.
Also, people who form bonds with others might exchange fragments of their fields, representing the emotional closeness and comfort one feels with friends and loved ones. In effect, the AT fields begin to "recognize" each other, and "fit together" (bosom friends and lovers), because elements are shared between the individuals.
This all only plays out in a non-corporeal realm, without conscious control, for normal humans, where time and space has no meaning- physical/geographical distance may not affect the interaction between souls, if the emotional bonds are strong enough, and active communication (of any kind).
What Rei and Kaworu, and the angels do takes they conscious manipulation and observation/sensing of souls to another dimension/level, where the physical world can be affected.
Okay, enough of my metaphysical musings.