The reason your getting such different answers is there are lots of variables that effect this.In my town the Justice gives the tenant 1 week to vacate.
The lease your parents signed, this could include provisions for eviction, meaning the time you have to vacate after eviction might be in the lease.
Some lease agreements include a stipulation for the use of your security deposit if you don't pay and give you another 30 days.
If your parents paid First AND Last months rent before moving in that should give you a month after the first missed rent.
The eviction laws are different from state to state, so the state your in will matter to how long you have.
A big city might have a long wait for a court appearance, a small town might do it the same week.
There are just so many things that can effect this...It's hard to give a specific answer without knowing the details...
I'm sorry that your family is in such a scary position. It's really sucky that your family might be homeless...But, you might want to get ready to face that. It's better if you plan it, prepare for it. Don't wait till the last min. It can happen, and most shelters are absolutely packed right now, and many have a waiting list.
If it's a big house with lots of stuff, and your broke and about to be homeless-you should probably consider selling it all. Better then losing it all and getting nothing for it. Just a thought.
Sorry I can't be more help, good luck.

