Oozaru

Is the first of all Transformations of the saiya-jin race. It happens when a Saiya-Jin sees a full moon and then becomes a large ape like creature. Any Saiya-Jin can turn oozaru no special training is needed, all that is needed is your tail, if you have no tail or it was chopped off, you can not go oozaru.

SSJ (super Saiyan-Jin)

SSJ is the hardest to acquired but is not the strongest. Goku was the first to go SSJ(excluding Broli) but shortly after Vegeta goes SSJ.

USSJ (Ultra Super Saiyan-Jin)

Is not really a SSJ level but I might as well add it, USSJ is a Buffed up verison of SSJ and SSJ2 with slight longer hair, you become stronger but you lose speed witch is the reason Goku did not stay USSJ for long. 

SSJ2 (Super Saiyan-Jin 2)

SSJ2 is reached by anger witch Gohan was first to reach. The hair gets longer and the muscle mass increase somewhat, You Glow a slight yellow witch is often followed by a Silver bolts

SSJ3 (Super Saiyan-Jin 3)

SSJ3 is also one of the hardest levels to reach, you much train very hard. your hair becomes extremely long about  knee level, SSJ3 does not have many up sides besides the Up in your power level 

SSJ4 (Super Saiyan-Jin 4)

SSJ4 is the Strongest level there are also no downsides to going SSJ4 Goku was the only real person to go SSJ4, you become ape-like again your hair stays but you are covered in red fur and your tail grows back!!!!!! (unless you still have it)