I feel your pain. I've had to deal with noisy neighbors before too, so I know how aggravating it can be.
The very first thing you must do is to ask your neighbors politely but firmly to turn down the noise, and to not move your stuff on the lawn. If they refuse, contact the landlord. It's his/her responsiblity to make sure they comply. If these actions don't work, you have to prepare to go to court and force them to comply, or if you don't want to deal with a lawsuit, simply move out.
If you decide to go to small claims court, you need to do is start collecting evidence. You will be suing for nuisance. Write down every instance of noise violation (e.g. when they play their music too loud) and the time/date, and other acts which you find annoying. Get a video camera and record all these instances. Before you can go to court, you will need to be armed with this type of evidence, so gather as much as possible. Get witnesses too, friends, other neighbors. I'm sure the music is bothering other neighbors as well. Perhaps you can talk with them and form an alliance.
Please visit the following links, which will be useful:
http://apartments.about.com/cs/neighbors/a/noisy.htm
http://www.tenant.net/Other_Areas/Calif/misc/noise.html
Under no circumstance should you have to endure their bullshit. You are paying rent to live peacefully, and if these people are so selfish and disrespectful, you do not need to be shy about confronting them. They need to be dealt with. If you stop them now, you will be doing a favor to other future tenants who will be living next to them.
Also, what makes you suspect they are abusing their dog? To me, this is a very serious issue. Gather as much evidence as possible, and report it to the spca or local police.