Deb, I don't know if this is feasible for you, but could you keep her on her leash and attached to you while you're in the house? You tie her leash to your belt and make her stay with you wherever you are. I admit I don't have experience with this technique - I read about it in one of the Monks of New Skete books when we got our puppy. It's supposed to improve trust and bonding with your dog and of course it would prevent house messes. ;)

Sorry I don't have any first hand knowledge, but best of luck and I'm glad you rescued her!
KCC

With her being a stray for the start of her life, I'd imagine it would take a while for her to get used to her new life with people and she was used to eliminating whenever she felt the need. Maybe she gets fearful when you leave the room and that causes her to act out. Maybe taking her out where she can be around people more would help her get more socialized and comfortable with her new life. I am by no means experienced, so those are just my thoughts. She's lucky to have you guys. Try finding a dog only forum and maybe you'll get more answers. I wish you the best!

I would suggest treating her as if she were an 8 week old puppy. She needs to learn how to be housebroken. Also, take her for a walk. Don't just put her outside and expect to know what you want her to do. Take her for a walk. When she potties, praise her like she's won the lottery. Crate her when you leave the house, but do as kitcatclub suggested and attach her to you.

You could also enroll her in a "puppy" obedience class to get her socialized with other dogs and they would be able to help you teach her what she needs to know.

This will not be easy with such a timid dog. It will take a lot of patience, but since you love her already, that is a good place to start.

Good luck.

She needs to gain some self confidence and how you go about it will depend on how extreme her fear is and if you're giving her lots of sympathy you could be making her insecurity worse. There are excellent training books/videos available and if you like Caesar Milan then watch his show for possible solutions. Contacting a local dog trainer is another option.

The 2 breeds she has in her are dogs that need LOTS of exercise and both are also working breeds. Take her for long, active walks and take her to a dog park so she can run with other dogs.
Do as murraysmom suggested and enroll asap in an obedience class and hopefully the instructor can give you some one-on-one advice. Just socializing with other dogs and people will make a huge difference and may be all she needs....along with basic house training.
One tip: before taking her to class, make sure she gets some exercise first so she can release some of her pent-up energy. IMO, that's probably her number 1 problem....no way to release her energy.
DS owns a Boxer and that dog can race around like a greyhound on crack! Luckily, they have acreage!

When I've fostered a dog that did exactly what your dog is doing I built a makeshift play pen over in the corner of the room everyone would be in the most. The dog had two choices when in the house (in the beginning), either be in the crate or in the playpen. He wasn't allowed out until he learned to calm down and control himself. He never got perfect at it and he ended up going to home that didn't want him in the house that much. He could not be trusted to run loose in the house without a human right beside him. Deep down I think he was just so insecure that he needed someone to rule him every step of the way. It was exhausting but after a month or so he started to get used to everything.

Just because your dog is timid and easily disturbed doesn't necessarily mean that it suffered abuse at the hands of a human. It probably did get pushed around by the other dogs but most dogs that get severely tortured by humans, get killed by those same humans. It is common to hear someone say their dog is an abuse survivor but I doubt they ever make it that far. Neglected dogs are a different matter and the mental damage done by neglect can make them act out like your dog is.

First Kudos to you for adopting.
Second while you have gotten some good replies you need to know you may never have a "normal" dog some dogs are not wired right and when they experience neglect or abuse, it just gets worse.
Having said that, here is my suggestion.
Go get yourself a bottle of Rescue Remedy and start with 3 drops into her mouth in the morning...this may help her with her anxiety.
If you catch her doing something like submissive peeing or eating something she isnt suppose to, try not to react too much (I know it is hard) if she is chewing a book, just tell her to drop it, and pick up one of her toys and tell her to play with that. Redirecting your dog by letting it know what is good and what you want it to do is key. To often we just tell them what not to do. Especially with your dog she needs to know what is okay.
As far as her seperation anxiety goes, dont leave her. Even to get a cup of coffee, having her come to you is going to reinforce the bond and in her eyes is is another positive - you may have to actually put a leaash on her in the house and just either tie her to you or pick up the leash and have her come with you everywhere.
You are going to need to stick to positive reinforcement behavior training. I suspect taking her on leash walks a couple of times a day will also help - I do not suggest taking her to a dog park, she is wayyyyyyy too unbalance for that.
The more you teach her what is hers and what is okay for her to chew on and that you want her to come with you while you are moving about the house and the more stupid pet tricks you teach her, the more confidence you will be building. Stop the Rescue Remedy if she starts to diengage or withdraw at all. Good luck and please post to let us know how things are going.

Listen to Mazer. She needs to be encouraged, praised and rewarded for appropriate behavior. (All dogs do, but especially a sensitive dog!)

She also need to be stimulated and kept busy if you are gone. Soak her food, mash it and stuff it in a kong. Freeze it overnight. Or get her a "Busy ball," so she has some kind of stimulation when she is alone. Make sure she has something to play with, gnaw on when you leave her alone.

A bored, nervous and un-excercised dog will redirect itself to unproductive and destructive behavior. She needs to be exercised mentally and physically.

Here is a link that might be useful: rewards / exercise toy