So I have an existing wire(ground,black&white wire) hanging along the dryway in my garage and I am trying to install a new 4 plug outlet on an adjacent wall.

I have shut off the breaker, spliced into the wires, added an external box(mounted on the outside of the drywall) and then ran wires along the wall to a new 4 plug box (this is the new box I'm trying to install)

So, in the box, where the existing wires are I cut black, peel back some of the insulation and then add the new (romex) black wire along with the wire I just cut, therefore having 3 black ends twisted together and finished off with a wire nut, same thing for the white and ground wires.

In the new 4 plug box I attached the black wire to the plug, the white wire, also and then attach the ground, then I take about 6" of wire and attach the one 2plug outlet to the other 2 plug outlet, same as before by attaching black to the side of one plug, then the other plug, same with white and ground.

When I turn on the breaker, smoke came out of the new outlet and now nothing works at all. Did I blow something at my breaker box? How can I fix this?

<cleaned up a bit line breaks = KISS>

Sounds like you made all the connections right (assuming you connected the black wire to the brass screw and the white wire to the white screw.) Why did you cut the existing wire? Couldn't you have tapped into an existing receptacle?

You probably have the bare ground wire touching a hot wire in the box. Take it apart, and carefully put the receptacles back in, making sure the ground doesn't come into contact with the hot.