The tau are not soulless, but neither are they psykers. Their signature in the warp is very faint, barely registering at all.
Other races? The eldar are universally psykers, although only a few actually make use of their psyker abilities in any significant way (warlocks and farseers). Others may use minor telekinetic or telepathic skills in conjunction with eldar technologies, but apparently there is far less risk involved than in the war related powers.
Orks also register in the warp, but they tend to generate a latent psychic field around themselves which is most evident in the power of the Waaaghhh! and is channelled most notably by the orks known as wierdboyz. In essence, the wierdboyz drawing on the orky waaaghhh energy functions similarly to other psykers drawing on the warp energy.
Tyranids, similarly do not draw directly from the warp, but rather from the Hive Mind. The Hive Mind presumably occupies the warp, accounting for the shadow in the warp that blocks astropathic communications and interferes with other psychic activity. Similarly, tyranid psykers drawing on the Hive Mind`s energy works the same way as a psyker using the warp again. There are hazards and occasional mishaps if a creature tries to channel too much energy.
Necrons... The necrons themselves are not psykers, nor do they register in the warp, being essentially machines now. But for the necrontyr before, nobody knows because they are never really explained in this sense. The one clue to this is in
Hellforged, where the Soul Drinkers are attacked by Necrons and Sarpedon fights a Necron Lord. The Necron Lord is vulnerable to the marine`s psychic attack because it is one of very few necrons who retains memory of when it was alive.
"You have a soul. Or at least you used to..."
I've been trying to look at fluff about psychic inquisitors and have a couple of questions:
Do potential inquisitors who are psykers get sent to different ordos depending on their specific psychic talents?
How much would the psychic training differ between the ordos?
Which of the ordos has the highest concentration of psykers?
Inquisitors recruit potential acolytes based on their own judgement, so I assume any ordo could use any level of skill. I do understand that the Hereticus tends to frown upon the use of psykers, but there are still psychic witch hunters according to the codex.
Also be aware that an Inquisitor of any ordo can end up fighting any foe. Eisenhorn for example is an Alien Hunter but ends up doing more work in the line of Hereticus than actually hunting aliens...