What type of switch would disconnect 3 separate lines?
A triple pole switch would be what you are looking for in this case.  You could also use a single-pole triple-throw switch.  Just take a look at the picture below:

 

You can use only one line at the time which I am assuming is what you would want to do.  Look for relays that are triple-throw if you want more information. 

But if you look to disconnect three lines at the same time, you would need to look for a triple-pole single-throw type of device.  Take a look at the one shown below:



This option would make more sense if you are trying to disconnect all the lines at the same time.