The Black Onion Squad is a 100 member private police force employed by the Ootori family. They are similar in nature to the Green Berets and are experts in martial arts. Their first loyalty is to Yoshio Ootori; however it is seen throughout the anime that Kyoya is also able to engage their services when it is not in opposition to his father's wishes.
The Black Onion Squad is a highly trained group of individuals who are proficient in multiple forms of combat, including the Haninozuka style of fighting. They are called upon several times during the anime for various reasons.
The first time they are mentioned is in Ep 01 - Starting Today, You are a Host! when Kyoya tells Haruhi that escaping her debt is impossible because she doesn't have a passport and he has access to the squad. Haruhi is simultaneously impressed and terrified.
The next time they are seen is in Ep 07 - Jungle Pool SOS!, when their help is enlisted by Kyoya to search the Tropical Aqua Garden after Honey is swept away by a tidal wave that engulfs him following a head-on collision between Tamaki and a totem pole that triggers the response in the wave pool's control center. Mori and Haruhi are confronted by the squad as they search for Honey who suddenly appears and attacks the squad believing that his two friends are in danger. The squad apologizes profusely and begs forgiveness of Honey as the most capable practitioner of their martial art.
In Ep 08 - The Sun, the Sea and the Host Club! they re-appear in a large box truck, bearing fresh shellfish by the dozens which they distribute onto the previously-empty sands where Haruhi and Honey are shellfish hunting. They do so with Kyoya's express permission in recompense for attacking Mori and Haruhi in the previous episode.
They are not seen again until late in the anime series in Ep 23 - Tamaki's Unwitting Depression! when Kyoya tells Ritsu Kasanoda what will happen if he exposes Haruhi's secret and, finally, in This is Our Ouran Fair! in which they are given direct orders by Yoshio Ootori to prevent the Host Club from following Tamaki, after he leaves for the airport with the Lady Éclair Tonnerre. Kyoya learns this when they suddenly appear in the school's garage immediately following Kyoya asking an Ootori chauffeur to help them follow Tamaki's rapidly disappearing vehicle. His fury at his father's meddling causes him to smash his fist on the limo's hood and to challenge the orders given to keep them stationary. With the help of the rest of the Host Club, he finds an alternate way to go after Tamaki; meanwhile, Honey and Mori jointly give a lesson to the squad about why it's not a good idea to annoy the Host Club.