Some specifics about research and teaching statements
I can tell you about what's normal in math.  


It's uncommon to depict your research areas in the form of a diagram.  However, if you are studying interconnections between different kinds of objects, say, a diagram may be appropriate.  Of course figures/tables/graphs can be very useful in illustrating your research.  If you include a diagram, it should be worth more than filling the same amount of space with text.
References to the literature are standard, and makes your research statement look more professional.  I don't think people actually go look up these references, but if they know the area, they may check to see what papers you refer to.
One or two quotes is fine, if they truly express a key point better than you can yourself, but more is not a good idea.  The more quotes you have means the less you personally have to say, and this is supposed to be a personal statement on teaching.  (Quotes from student evaluations etc are a different matter.)


In any case, it's a good idea to have colleagues/mentors that you trust take a look over your application material for feedback.  This way they can let you know if you've done something crazy, or if things are just unclear.