The kuijins' major power is that of morphing into the shape they want.
There are, of course, limits to this power. For one, kuijins often choose no other than one second form (aka phorm or morph) (aka a form, different from their base form or original form, which they adopt for reasons of abilities or fitting in); the process of morphing can be very complex depending on how different the second form is from the base form, and so kuijins cannot memorize more than one transformation. Some kuijin decide to learn many simple changes instead of a single large one, usually because they have no need to hide their true shape.
Another limit is the speed and quality of the morph. The young a kuijin is, the slower and simpler the morph will be. They are not yet familiar enough with the second form to quickly change into it, and have not yet been able to reach the level of concentration needed to change a very large part of their body. To morph, kuijins have been given the ability of changing the properties of their cells (in other words, they can change a muscle cell into a bone cell), though they cannot change their number (so their mass stays the same, even if their size doesn't*), and so need an amazing amount of mental strength to undertake a morphing. Only older kuijins, who have familiarized themselves with their phorm, can change quickly and with more precision. However, certain kuijin never learn how to make a shape which resembles more than remotely what they want, meaning that they must hide themselves with long-sleeved, baggy clothing or veritable tents of fabric.
About the first form/base form:
This form is usually determined by what the parents were. If the pair was made of an eagle and a crow, the offspring would probably be a mixture of an eagle and crow. Though it is rare, the child could also be something completely different (these are called Originals: they strongly resemble the actual animal their soul is based on, and are very prestigious to have around as they are often believed to be incarnations of the First Kuijins**). However, if the parents were an eagle and a lion, it would give a hybrid (pairings like this have never given an Original) which probably resembles a griffin (fore part of body is bird, hind part of body is lion). BASE FORMS CANNOT BE TRUE MYTHICAL CREATURES. Humans saw hybrids and gave certain types names (griffin, dragon, unicorn), but hybrids do not possess the true mythical creatures' magical powers - they only look like them.
NOTE: Though many kuijin decide to take a human as a morph/phorm/second form, this does not mean that they are humans who can turn into animals. They are animals, though strange and not truly realistic animals, who can turn into what they wish to, be it a fish, an eagle or a human.
* Because of this particularity, insect kuijins have been known to create 'shellmen' when taking a human for second form, unless their base form is absolutely massive. Since insects simply have an exoskeleton and some vital inner organs, their mass is very small compared to their size, meaning that a true human would look much too small. To look normal, insects need to leave empty spaces inside their human form, meaning that when they are killed in human form, these spaces are apparent to whoever's shot their chest in (yum, gory bits).
** See Legends and Religion.