That setup is so f'n amateur hour it's disgusting. Why the hell are they using TWO single gang plates inside a double (or whatever) ring on the wall? Why is it not two separate single gang old-work rings or one double-gang ring with the wiring installed properly?
You will want to check each single speaker connection and ensure that it goes out to a speaker in your home. If you have an existing AV receiver than you can hook up a single left or right channel one by one by one. You should hear audio playing from a speaker, and you should specifically label each speaker location for what it is.
From there, you will have to decide what exactly you would like to do. Be aware that getting TV audio from your upstairs TV down to the system, and back up to in-room speakers in not a task for the lighthearted and is typically way beyond the typical person who isn't comfortable with whole house audio distribution. But, if you have a cable box up in your room, you would need to use a network or cat-5 point to point extender to get audio out of the TV or out of the cable box back down to your distributed audio head-end.
In reality, most people design the speakers around 'whole house audio' and completely ignore the video portion. In my home, I have not. I integrated both audio and video, but it was planned that way from day one.
If your goal is just to be able to play different music, or the same music, in different rooms, and control the source and volume in that room independently, using your phone, then you will need a whole-house audio system, like those sold by Home Theater Direct. They offer fairly inexpensive, phone controlled, units that will give you independent amplification for up to six separate rooms and allow you to connect up to six analog audio sources to it.
Whole-house audio systems you can install yourself and control with smart phones and tablets. All HTD systems include a 30-day guarantee and 5-year warranty.
www.htd.com
If you keep asking questions, you will get answers here. It is not straightforward for everyone, but at least you went so far as to pull things off the wall and take a look at things.