The housing and rental market is VERY tight in the Portland metro area. Rents are high, and landlords are extremely picky. But I think with patience you can find something decent. Here's my advice:
Don't bother with apartment sites. They run a scam on applicants here, and it's apparently legal, regarding the deposits and application fees etc. They snare people who don't have easy options, and the process is demeaning and ugly and very costly. Look instead for places offered by individuals. Could be a duplex. Couple be a walk-in basement. Perhaps even an apartment in a private home, with utilities included. What you find first doesn't mean it's your *forever* place. Just getting a foothold could be the immediate goal.
I read craigslist every day for two years and finally found a dream of a place. Just a dream.
So I suggest that you read craigslist every day just to learn what's out there. As the time gets closer, you can zero in and hopefully make something happen. You don't say where you hope to find work or if you want to be in the city or outskirts.
I don't believe you will find easily any assistance programs for low-income or disabled -- the waiting lists are long. There are programs that can help with energy assistance, etc. though.
I would recommend that (unless you are set on big-city living) you look just south of the city in Gladstone, Oregon City, or Milwaukie. Or perhaps east of city in Gresham. Why? Because outside of Portland's zoning restrictions, there are many more unique housing opportunities. Lots of older neighborhoods with fixer-uppers and modest alternatives. Crime is not an issue, people are friendly (it's kind of like stepping back a couple of decades), pets are more tolerated, etc.
You don't mention whether you have reliable transportion. But metro Portland's public transit is legendary, even despite some recent budgetary issues. Light rail runs to Gresham, and soon will be available to Milwaukie. Commuter bus service is available to Gladstone and Oregon City. You can even ride Amtrak from Oregon City to downtown Portland. A monthly metro transit pass for a disabled person is only $26 -- that takes you anywhere, any time for a whole month!
A couple of other thoughts: the Oregon Health Plan is also legendary. You may qualify for that. You may qualify for food stamp assistance? There are half a dozen food pantries in the areas I have mentioned, to supplement grocery needs.
Oregon City is a wonderful historic town. Right on the river, it is literally the end of the Oregon Trail. It has a newly rejuvenated downtown.
Las Vegas sounds like a nightmare these days. Anything I can do to encourage you, I will. I don't generally like to urge lots of people to come to Oregon (we don't want it overrun, ya know). But you sound like good people, and you really really need a break.
Feel free to PM me.