To be honest, Bleach and In Nomine are incompatible. The power creep is entirely too steep within Soul Society and Hueco Mundo – especially given how static both locations supposedly are.
However, crossovers are fun.
So here’s my take on the Soul Society based on the earlier seasons (where a handful of exceptional children fresh from the mortal world are able to challenge the status quo).
What is the Soul Society
Within the setting of In Nomine, the Soul Society would be an ethereal domain styled loosely on medieval japan and populated almost entirely by Dream Shades. Most residents chose a comfortable life of manageable labor, but since they are now Ethereal beings, some develop Elements & Affinities. The Shiba clan, for instance, tends to seek out those with an affinity for Destruction.
In order to become a Soul Reaper, a denizen of the Soul Society must first be able to summon their sword, the zambato (in other words, they must have a moderate Affinity for either Puissance or Artifacts).
Most Soul Reapers also learn a number of Kidou (songs).
The Soul Reapers have three main functions. They are the peace keepers for the Soul Society, it’s military force, and they occasionally cross over to the mortal world to ease mortal transitions into death so that a soul traumatized by abandonment does not become a monster (known as a Hollow).
A Dream Shade generally cannot past the rigorous tests necessary to become a Soul Reaper without having first built itself back up to at least 5 Forces.
To get a numbered seat in one of the 13 guard squads, a Soul Reaper must be able to manifest a strong Affinity, which also means at that they must have at least 6 Forces. In most squads 7 or more Forces are required to be ranked, but the 4th (for example) favors ability as a healer over almost anything else.
Lieutenants generally need to be around 9 Forces, and those who want special assignments or to be considered for promotion to Captain generally need to have Awakened (represented in the Soul Society as releasing a bankai).
With one or two notable exception, all of the captains have Awakened and have at least one Primal affinity. In theory someone could make Captain with only 9 forces, but the process is highly competetive, and Captains can theoretically go as high as 15 Forces (human maximum).
In addition to the 13 guard squads, all members of the Royal Guard are considered Captain rank, as are the heads of the Kidou Corps and the Secret Police.
The Soul Society has four noble houses. Each generally has a handful of Elements they look for in new Dream Spirits. Those who possess several Elements aligned with a noble house are deemed superior and given a special place within the Soul Society, though they must still meet the minimum qualifications of a Soul Reaper to join one of the 13 guard squads.
Kuchiki Clan (Favored Elements): Astrological Concepts (Stars), Information (Knowledge), Society (Nation/Nobility)
Shihoin Clan (Favored Elements): Astrological Concepts (Moon), Life (Animals), Wealth (Heirlooms)
The other two Noble Houses have not been detailed, but it’s safe to say that at least one of them is interested in Dream Shades that have developed a Sun Element.
A group of 40 wise men and 6 judges selected from throughout the Soul Society. Although they tend to have higher than average Ethereal and Celestial Forces, very few are Soul Reapers. They serve the four noble houses and the Soul King.
The Soul King
An unseen and bound being who is afforded great respect but limited freedoms. He regulates the flow of souls between earth, the Soul Society, and Hueco Mundo (realm of the Hollows and Arrancar). He is one of the few forces in the world of Bleach who might reasonably be considered a Superior. Possibly the Archangel of Death (who is conspicuously absent from the canon In Nomine texts).
Arrancar are Hollows who managed to partially remove their own masks. As a result Life and Struggle affinities are especially common among the Arrancar, as are Emotional Affinities for things like Fear, Pain, Hunger, Emptiness, Rage, Sorrow and Ambition.
“Natural” Arrancar are probably around as powerful as Soul Reaper liutenants (8-10 Forces, not awakened). The Espada are artificially created, Awakened and easily rival most Captains.
While the Arrancar are hollows who have gained Soul Reaper like powers, Vizards are Soul Reapers who found a way to become more like hollows after reaching the soul society. With the exception of Ichigo they are all criminals and all awakened.
The Bleach comics at one point released Battle Data on many of their characters. While attributes do not have a clean alignment with those of In Nomine, they can yield some quick and dirty stats for the Captains. Because the Soul Reapers are all human souls, 100% equates to a 10 and scales accordingly.
Offense → Precision
Defense → Awareness
Mobility → Agility
Reiatsu → Will
Intelligence → Intelligence
Physical Strength → Strength