Omori Ryu no longer stands as an independent ryu-ha. It exists in its extant form through its inclusion in both Muso Jikiden Eishin Ryu (MJER) and Muso Shinden Ryu (MSR). In both of these ryu-ha, Omori Ryu exists as the shoden set. Omori Ryu is considered koryu bugei and is exclusively iaido.
The ryu-ha was developed by Omori Rokurozaemon Masamitsu, originally a student of Hasegawa Chikaranosuke Eishin, for whom the chuden set of both MJER and MSR, the Hasagawa Eishin Ryu, is named after. Omori Ryu takes aspects of the Osagawara Ryu Reishiki (a school of ettiquete known mostly for popularizing the seated position of seiza), Bishu-den Yagyu Shinkage Ryu, and what Omori had learned from Hasegawa. Omori was apparently expelled by Hasegawa, but upon his innovation, was allowed to rejoin. His techniques were thus incorporated.
Omori Ryu contains eleven or twelve kata depending on which art it is practiced as a part of. As a whole, they are referred to as seiza no bu, meaning they are all are performed starting in seiza. The kata are as follows, with the MJER names first, MSR second, translations in parathesis:
1. Ippon-me - Mae (front), Shohatto (first draw)
2. Nihon-me - Migi (right), Uto (left draw)
3. Sanbon-me - Hidari (left), Sato (right draw)
4. Yonhon-me - Ushiro (behind), Atarito (striking sword)
5. Gohon-me - Yae gaki (eight-fold fence), Inyoshintai (Yin Yang mind and body)
6. Roppon-me - Uke nagashi (flowing block), Ryoto (flowing sword)
7. Nanahon-me - Kai shaku (seppuku assistance), Junto (assisting sword)
8. Hachihon-me - Tsuke komi (seize the opportunity), Gyakuto (reverse sword)
9. Kyuhon-me - Tsuki kage (moonshadow), Shinchuto (true motive sword)
10. Juppon-me - Oi kaze (wind chaser), Koranto (running tiger sword)
Here, MJER and MSR start to differ in structure. MJER finishes with:
11. Juippon-me - Nukiuchi (sudden attack)
MSR has an additional kata:
11. Juippon-me - Gyaku-Inyoshintai (reverse Yin Yang mind and body)
12. Batto / Nukiuchi (suddent attack)
The original set seems to match that of MJER, that of eleven kata, which makes sense in the sense that the twelfth kata is (upon first inspection, I know not the subtleties) a variation.
The MJER names were changed by Oe sensei upon his formulation of the ryu-ha. The MSR names are the originals.
Each kata has numerous kaewaza, or variations. These variations are mostly unnamed but they are still taught through oral transmission. Counting all of these kaewaza would bring the number of kata to around 45.