OK, LL can list house for rent while tenants are still in it, but NOT in middle of lease.
If this is Section 8 housing, go talk to your housing counselor.
Is your rent current? SEction 8 won't give approval for another tenant if she isn't treating you right.
If you have lease, LL cannot tell you to just move out. You have rights, and lease sets time when you have to move out, when lease ends. Even without a written lease, you need 30 days advance notice. LL must give you 24 hours notice in advance of showings, and if there is serious problem with showing you need to contact the LL. You being still in house is OK, still packing is OK. LL did not have to give you an option of month to month. If she said you couldn't break your lease, what is going on now???
LL can show house if it up for sale or when your lease is ending.
You're NOT giving us all the information here. Why is LL telling you to get out without giving 30 days notice? So you paid the July rent in full, but late (yesterday)? Let her file in the courts, because If she files in the courts, you won't have to be out until late August, or end of August. So don't let LL PUSH you without reason. Of course if she gets court ordered eviction that hurts your ability to get another place.
Anyway, calm down, talk to Section8 counselor, get legal advice, etc.