I started reading some responses... but I'll just give you the advice that I have. I had my condo on the market for over a year. Part of that time, I was still living in it, part of the time, it was empty, and for the last few months (before I decided to take it off the market), I had a tenant in it. I hated having to keep the house in "show condition" in case a potential buyer wanted to see it (I had a realtor handling all of that, but there was a lockbox). Especially with pets and a young child and a full-time job... it was hard keeping everything so clean and organized! So, I can understand the frustration of that (having people come into *your* home). When my tenant was there, the lease stated that I would provide 24-hour notice before entering the property. I extended this to the realtors, too. In other words, they had to let me know at least 24 hours ahead of time of a scheduled showing--so I could inform the tenant.
It sounds like you've had a really bad experience in this place, and I do know that there are landlords out there like that--who are just in it for a quick buck and have no respect or consideration of their tenant's living conditions. It's good to hear that you'll be out of there soon anyways! I hope you have documented everything that has gone wrong with the place so that you can get your deposit back.
My suggestions are:
Re-read your lease--does it state a minimum 24-hour notice for entry? If yes, then you can decline showings that do not give you enough notice.
To ease your pain, I'd leave the sign up and place the lockbox. But, only provide the key once you've been given the proper notice (assuming your lease states 24-hours). You can claim the security risk to your family and belongings.
Pack up as much as you can, as quick as you can! You'll be leaving in about a month anyways. Start putting away your winter clothes & blankets. Pack the least-used kitchen wares. Move the boxes to the garage once they're packed--this will make it much easier to "show" the house.
You're right, this shouldn't be your responsibility. As for the state of the house... you probably shouldn't directly say anything to potential buyers, but I don't think it would be all wrong to leave out a random bill or such... Heck, when we bought our house, there were notices from electricity and water for past-due bills (the house was bank-owned and *somebody* hadn't paid the bills)! Just take care of yourself, get out of there as quickly and painlessly as possible and count your blessings that nothing bad happened there (electrical fire, inablility to pay bills, etc).
Good luck, mama!