I'd recommend walking into a couple homeless shelters, volunteering there and getting to know the user base. I'm sure you could get some face time with a director or staff there and ask them what they think about your ideas. I bet they will have a lot of feedback for you. One of their primary jobs may be to connect their clients to the community and each other -something you are trying to do too.

I have spent a fair bit of time in homeless shelters and working with immigrants so I'll share a bit of my experience there. I bet more homeless folks have cell phones than you may think. If they are in an urban area, they will likely be able to get access to the internet via wifi. A number of homeless I have known have a cell phone with apps and use it for texting, but don't have a phone or data package.

If you're hoping to connect homeless & refugees to jobs, then you'll need to connect them to the established community and not just each other.

App or website ... If it's a social app, is it something they'll need connectivity for all the time in order to use? If so, then you could probably go either way. If they could technically use features of the application offline, then you could go the app route.

I've done a lot of volunteer work in this area so I'd be curious to follow along how you're doing if you have things to share.