What are my options on not signing a lease for a room I rent at my sons?

To begin with , they can't throw you on the street at the end of the month! There are eviction regulations they would have to follow. (thinking of the recent news item about the 30 year old son that parents took to court to get out of their house!)
Just about EVERY place has senior housing where rents are based upon income. Can you call your county office of aging and see what is available in your area. There may be a waiting list but add your name to it even if it seems impossibly long.
Do you have other children? Friends? Many areas have transportation services that may help you get around. How old are you? Any health issues?
It appears that you went along with your son's game plan. Are there additional pieces of information that would give us a clearer picture? For example, if you are 78, no health issues and paying $100/month rent ---- I would view the situation differently than if you are 62,paying $600/month rent.   Are there other assets?  What happened to the proceeds of the car sale?  

I cannot comment directly on your situation. But there have been many posts here about needing proper documentation for rent being paid and what it covers, especially if Medicaid maybe needed in the future. Otherwise it looks like you have been gifting your kids.

From your post it looks like the only change is paying 1/3 of the internet and cable bill. Is the extra so onerous that you decided not to sign a lease? How much would it cost you to live on your own? Are you paying the full amount of the gas and electric bills or 1/3?

I do not know why you agreed to sell your car, but it is unreasonable for you to expect your family to drop everything to drive you places. Just as it was unreasonable for my teens to expect me to drop everything to drive them somewhere (except in an emergency). Most communities have some form of seniors transport. Grocery stores deliver, taxis can be called.

How long ago did he present you with the lease? What are the tenancy rights in your state? If he told you today that you have to be out in 10 days, that does not seem fair or legal.

What is it that you want to do? Live independently again or renegotiate the terms of living with your son?

There doesn't seem to be any love lost between the two of you, why would you want to stay? I agree that since he has chosen to treat your relationship as one of landlord/tenant then you need to know your rights as that tenant - two can play hard ball. This arrangement clearly isn't working for either of you, to preserve whatever you can of your relationship with your son I think you should attempt to negotiate - perhaps with the help of a third party - a reasonable amount of time to allow you to make the necessary plans to retake your independence and find your own place.

I pay ALL of the gas and electric which runs between $150.00 and $250.00 a month depending on the weather. He has paid the cable and internet for the last 2 with no problem until recently when he came into my room and took the cable box and changed the password on the internet so that I can't use them unless I pay him. He agreed to help me buy a car when we got up here and then changed his mind once we were here. Like I said before I live on social security(around $1000.00 per month, buy ALL my own food and pay ALL of my bills on my own. While I was on a trip this month he sent me an overnight pkg to my other sons home with the lease and all of my mail( I was only gone one week June 6th thru June 13th) with no advance warning about the lease. He said I had until the end of the month to sign it or get out. There would be no negotiating what is in the lease. I don't expect them to just drop everything and take me places, but it would be nice if when they went to the store they asked if I needed anything of if I wanted to go also.That way when they did get home I wouldn't have to make arrangements to go buy groceries on another day.

Grnmaof6, there has to be a back story as to why your son was acting so quickly with the lease and turning off your use of the cable/internet. Apparently the internet issue was resolved some how so you could write on this forum.

The Lease is an excellent idea, as others above have noted that if in the future you should need to apply for Medicaid [which is different from Medicare] the Lease will show proof that you were paying your son money for rent, and not as a "gift". I realize all of this is new so so many people who are not familiar with the workings of Medicaid.

What was the reason for selling the car? Was the cost of transporting the car by truck would have been too expensive? I could see that happening. Maybe there is a reason that your son prefers that you not drive. Have you asked him?

At the very least, get independent legal advice. Your son is asking you to commit to a binding legal agreement. If he is doing this without giving you reasonable opportunities to ensure that what you're signing is fair and sustainable, then his attitude wants an overhaul.

That doesn't mean that it isn't a good idea for you all, as a family, to have everything down on paper - it IS a good idea for everyone to be certain of where they stand. This would also be a good time for you to discuss contingency plans for the future, such as what happens should you begin to need more support with things such as personal care.

But from what you describe, he's lost patience and is now going about things in a rather overbearing way. Don't let yourself be bullied; indeed, tell him that you won't allow yourself to be bullied. If you can't afford a lawyer or an elder care advisor, contact your Area Agency on Aging (or equivalent) and ask them to point you in the right direction.

And while you're on the phone to them, ask them if they know of any transportation services for elders that you might be able to access.