What you've encountered is commonly called a duplex with 'backstab' connectors. Switch devices also offer this connection option. Although simple to install, they afford a small area of actual metal contact for transfer of current, and can overheat, which is why no professional I know uses them. In essence, the device is being used as a junction, hence the six wires. Personally, I'd vote to have them banned in a heartbeat.
To solve your immediate problem, remove the wires from the rear of the receptacle, and install Ideal Term-a-NutŪ connectors
http://www.idealindustries.com/wt/Tw...Connectors.nsf duplicating the connections present on the device.
You may not find them in a big box store, but any electrical supply house worth their salt will have them.