Cant help on the portrait photography models but if you would like models for grittier genres try hiring homeless people. One shot i was thinking was have a homeless guy sit on a busy sidewalk, set camera to long exposure. You know where im going with this.
I'm going to disagree with this (respectfully). I am actually starting a social documentary regarding some of these issues through well established means (ie. shelters and a fellow I know who lives on the streets) and paying someone who is marginalized to take their portrait is not going to help them. Most people experiencing homelessness don't want to have their portrait taken first of all and secondly I don't see it necessarily being in good taste. There are always exceptions though so I don't want people to get all erked by this statement but please realize this probably isn't the best place to start. (For myself I have already been on two 'shoots' - really just walks around the downtown, probably 20 images were taken in total - with two different guys who live on the streets mostly just to learn more about the difficulties people who live on the street experience and it has been mentioned how disrespectful it is when people 'steal' their pictures. I know this isn't what you are suggesting but it is quite a sensitive issue).
Honestly. I would want to portfolio build with friends but if you honestly don't have anyone prepare some cards and ask people at your local coffee shop if you could take their picture. Since you don't have images for them to preview beforehand your hit/miss ratio will be pretty crumby but someone is bound to say yes