These are not actual fighting styles from Bleach. THe shinigami styles actually come from Star Wars, but can be used to describe one's style.
Shinigami Sword styles (Arrancar, Vizard and Shinigami only):
-Shi-Cho: the basic form practiced in the academy. based on old-fashioned swordfighting. The most deadly, if slow skill.
-Ataro: the acrobatic form. This puts spirit powers into one's reflexes, enchancing Flash step users. Ataro users can leap over enemies and are generally nimble and the fastest of the styles. Its weakness is Soresu.
-Soresu: the defensive style. This focuses on defending power and endurance, built to fight projectile weapons. Users can generally be skilled enough ot evade bullets or to block them.
-Makashi: the fencing style. The most elegant style, it emphasizes on precision and speed, and is the best style, good against all the others, excluding Soresu and Niman. Users use a one-handed grip, and is rarely used.
-Niman: the balance style. the most balanced style, it is best utilized with twin sword users. No weaknesses apart from its inability to block well.
-Djem So: the solid style. Built on Soresu, it puts Soresu's defensive power into offensive skills, making it the most solid style of all. However, users generally are slow, and are therefore suscpetible to Ataro.
-Vaapad: the most dangerous style. Vaapad is a style that takes the opponent's offense power and absorbs it, channeling it through the body and back out at the opponent. This makes it almost invincible if used right. However, the user must focus in order to channel the enemy spirit power without unwittingly damaging one's inner organs. Therefore, its weakness can be exploited by putting uneven power into each attack so that the user cannot cope. If used incorrectly, Vaapad can cause one's own death.
Quincy Styles:
Crossbow style: the slowest style. fires spirit energy from a crossbow. this makes the msot powerful shots of all the others, but cannot fire a lot of shots and has a slow reloading speed.
Shortbow style: the most-used and nimblest style. The shortbow is easy to carry, and si often used. users are generally fast and can shoot on horseback. however, it's weak power makes it weak, and it lacks range.
Longbow style: These bows are the second strongest, but have the highest reloading speed and has the longest range. however, these bows are heavy and require a lot of strength to wield. Ishida Uryuu in bleach uses this style.