Well Michael is overly defensive against practically anyone who criticises him, hypocritical and self-centred, plus he wants it all: dangerous criminal lifestyle as well as an ordinary family life (unrealistic expectations.) So I'd say he's a narcissist based on his egoism as well as the fact that he's very materialistic.
Franklin I chose non of the above, can't call him a narcissist he is nowhere near as false as someone like Michael, can't call him a psychopath either because I Don't see delusions of grandeur or him getting a thrill out of killing, as for sociopath, he Isn't controlling enough over others, I.e. you don't see him manipulating weaker people through fear/bullying as you see Trevor do to Floyd or wade, plus the fact that he cares for an animal (chop) goes against the sociopath profile too. Yeah he does kill for a living but he doesn't get off on it.
With Trevor it's tempting to say all of the above, but the fact that he mourns Michael when he thought he was dead, the way he was with Patricia, also the way tries to please you know who after the final mission by getting her meds then having the breakdown afterwards shows a side that craves love and acceptance which is a bit of a counter weight to the more psycho/sociopath if aspects of his personality, it's quite hard to actually pin down what Trevor is exactly in it's entirety.