How critical is it to use the correct wire colors within the same electrical outlet?
The answer to your question is "quite critical":  Grounds must be green, yellow/green or bare.  Neutrals must be white or gray.  All others are hot.  

Binding stranded wire to a screw terminal is tricky. Not impossible but tricky.  I like to "super-twist it" by gripping  the wire in a hole intended to shear off bolts, which keeps it circular.  You have to have just the right touch to clamp the wire enough to hold it without shearing it.  

Because of the difficulty for a novice to attach stranded wire to a screw terminal, I would advise either going to the shop and getting some solid #12 wire, or, you can use round crimp terminals for the ground screw on the junction box (not on a receptacle).   

If you have wire whose insulation is not green or yellow-green, there are two ways to mark it as a ground. 


Strip all the insulation off. Optional: wrap it with green tape, which will solve the birdcaging issue if the supertwist doesn't. 
Don't strip the insulation off and totally obscure it with green tape. However this violates Code.