I have never had a problem with my address not being on my resume. Though I am having problems making contact via phone as 1) My phone is an old junk Android. 2nd Gen 2) I can only make and receive calls over wifi (had to cut cell service)
I am planning to work on my stackoverflow and other online profiles.
Thank you for all of the advice.
Also, don't worry about companies or recruiters bad-mouthing you to one another. It rarely happens for legal reasons.
About phones:
For phone issues, consider using google voice on your laptop with a headset ($10) and fixed Google voice number instead- this will be hard when you're on the move (can forward calls), but it will make sure you can occasionally have high-quality phone calls. I almost never needed to accept or make non-scheduled phone calls during my job search. To sign up unfortunately you'll need at least temporary access to get a verification call on a mobile or landline (but hopefully the shelter or a public phone can help with this).
Depending on how big a volume of possessions you need to carry with you, scout out all the Starbucks (which now allow use of their wifi and bathrooms without purchase) in a reasonable distance, to find one or two with quiet corners where you could take an interview. If the interviewers hear sound in the background, tell them you're in a Starbucks. If they ask why, say your roommates are loud so you tend to work from Starbucks. There shouldn't be any further questions about that.
Unfortunately, though, @jl2718 is right that many employers won't look upon OP's situation positively, and it's hard to tell if any will (except @leesalminen, who apparently will). Therefore some strategic non-disclosure of circumstances is advised.
Have you figured out what you're doing for your address? Do you have a nice set of clothes, haircut, and shave before interviews? If you don't put a residential address on your resume, it isn't going to help you.
I am sure you're already getting enough advice on the technical aspect of finding a job in this thread. You can know anything, but if you can't get through the door because humans are superficial you're still screwed.
I would do this: hit up freelancing websites and make enough money doing small gigs online to get an apartment or rent a room with somebody. Those sites have a bad rap, but I promise you I've done well enough on them to say it's worth your time. Accept a low rate at first to get feedback and ratings on whatever site you choose. Better freelancing companies also poach people from those sites. If you have a good profile, someone will ask you to come work with their clients instead. It happened to me.
Worry about creating a marketable image: your online profiles personal website, github, stack overflow, linkedin etc, your appearance (fitness will make you more marketable), and your sales pitch. Write a pitch and rehearse what you're going to say in interviews. They're going to ask you what you've been doing! My advice: don't tell them about your recent misfortunes. It might be true, but would you want to buy a car that had mechanical problems and was found abandoned on the side of the road, three years later? You'd want to buy a shiny new car. You need to become a (good) used car salesman and you will find yourself in a job.
Good luck in your search.