I've gone over Gaku Homma Sensei's book again (the relevant section ), as well as consulting my wife (native Japanese) and a work colleague with MA experience (also native Japanese). OK, here goes, forgive me if it comes out garbled.
Osu - means to push, or male of species with regards to animals, not humans.
Usu - is a large bowl used in cooking.
Osae - means to hold down or to pin, as in osae waza (ikkyo, nikkyo, sankyo etc.).
Osu/ usu can also be taken to be equivalent to "hey" or "oi you" or "yo". However, this term is mainly reserved for College students, primarily male. It is unlikely to be used outside of college and almost certainly not used when addressing a senior.
Is also used to fire up the kiai in some of the fighting arts.
With Regards to Homma Sensei's explanation, it's a three/ four page excert in his book. I've pulled out a lot of it but not the entire section, apologies for the missed bits, but I don't think they are needed. Also apologies to Homma Sensei for typing up his words, especially if they now seem out of context. The actual section that it is in is titled "Rei is easily misunderstood".
REI = RESPECT (for those unsure).
Homma Sensei was witness to a MA demo by the son of a friend, the son presented himself to Homma Sensei and bowed whilst saying ossu. Homma Sensei asked the boy what it meant, and was told a "a respectful bow". This is not true.
In Japan, ossu has come to mean something like "how's it going", but if you look at the origin of the word, the two kanji that form ossu (kanji characters not displayed) = push and patience. Literally translate to - "to be patient and be patient some more".
Why is it popular in MA dojos? not because it implies students would react patienly if attacked! During the samurai period, anyone caught practicing MA that were not of samurai stock were executed. The martial philosophy behind saying ossu was developed by the non samurai people of the era to protect themselves against violent predators of the era. This tradition was inherited by by post WWII MA students, saying ossu implies that no matter what happened to their body, whether punched, kicked. stabbed or shot, they would continue to respond by hitting, punching and doing anything possible as long as their bodies could function. More than anything else, ossu came to signify tolerance against pain, it became a declaration of fighting spirit based on self sacrifice.
He then talks about MA students using ossu to fire themselves up before breaking boards, bricks baseball bats etc.
This approach to fighting was not found amongst samurai warriors. When samurai fought samurai, there was an accepted code of conduct. Samurai had had to be prepared to fight at any moment, as a result, they paid close attention to their bodies and health. Self sacrifice in training was not considered a virtue, nor was risking the damage to their bodies whilst breaking bricks. bats etc.
Before two aikido students practice together, they each sit in seiza, place both hands palm down on the floor and with a straight back, bow deeply to each other as an expression of rei. This simple action is an integral part of our training.
In contrast to the practice of ossu, the practice of rei helps develop respect for all people.