Without a lease, it can get pretty hairy. If they have served a detainer warrant against you, you'll have to wait for your date in court, state the facts and see what the judge decides.

Consult with an attorney who knows landlord-tenant laws in Sullivan County. Such laws vary not just by state, but by city and county as well.

I'm not a lawyer, and I don't know Tennessee law at all, so this definitely is not legal advice. However, if you have no lease, then you are in a weaker position than if you had a lease that spelled out the rights and responsibilities of each party.

Further, you don't say whether you're living with your parents or in a separate property. (It might not make any difference, anyway.) In a separate property, it might be the case in some jurisdictions that there'd be an implied or constructive lease. (Even then, it could be that without a lease, you'd be on a 30-day notice.) However, if you're living with your parents, in their home, I'd suspect your case would be very, very weak.

Again, talk to a lawyer.

However, and this goes well beyond real estate, you and your boyfriend need to get your act together. I'm not a mindreader, but I am a parent, and probably as old or older than your parents, and I suspect your parents are pretty much fed up. I'm just guessing--and I'm not defending them or taking their side--but their perspective is probably one of frustration. You've got a boyfriend and three kids. They've probably talked to you about moving out, or to a place of your own, and you've kept promising to do so. Your boyfriend probably works sporadically, or changes jobs often, so there's never enough money to really find a place of your own. They probably didn't like your boyfriend to begin with, and those three kids didn't help. They love their grandchildren, but are frustrated with you continuing to make (what they believe to be) wrong choices in your life. They hope that evicting you will force you to face reality. (How am I doing?)

You, in turn, are wondering how they could be so cruel and heartless. You think they should accept your boyfriend because he is your boyfriend. They just don't understand that your boyfriend's had some bad breaks and bad luck. And you think they should admire you for sticking with him and supporting him; instead, it seems as if they're punishing you for being a good companion. (How am I doing?)

Although you didn't ask for advice on that aspect of the problem, it really is time for you and your boyfriend to make a life on your own. If you've been renting from your parents, you can rent from someone else. You're convinced your parents are wrong about your boyfriend and your ability to go it alone; prove it to them. Show them, by your actions, that you're right. Remove that whole area of contention between you and your parents.

Good luck.