The question is, what will be more efficient, to create the app, or learn more about lets say PHP and create the web, or maybe use a CMS as Elgg to create it
Early on you'll be doing a lot of A/B testing, making changes, getting feedback, making mistakes and so on. All of this is easier in a website.
Facebook's early app was considered a mistake and they "wasted" two years before they switched to native but I think they iterated like mad during those two years and really learned fast.
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.
Do you have an email? I will update you when I have talked to some shelters / homeless people and when I get some work done
The main problem here is that these people won't have an easy access to the internet so it might be easier a website but otherwise I think an app would be more suitable.
(probably worth go to the streets and ask them).