You can't it's very rare to get away with no soldering on a kit due to the power supply circuit designs, while some ESCs and motors come with pre-fitted connectors, (many will just solder the motor wires direct to the ESC), the wires connecting to the PDB will need soldering anyway.
I used these ESCs, (there's also an OPTO version if you want to use the 5volt output from your PDB to power the Naze, Rx, Etc.), but it looks like you'd have to solder the bullets onto the wires from the motors anyway.
Anyhooooo, your question about soldering the connections;
The servo leads and connectors are already fitted, and just plug onto the Naze.
The 'input' power leads on the ESC, (the RED and Black), will need soldering on to the PDB, (b.t.w. you appear to be missing the battery to PDB lead also from your list).
To join the motors to the ESCs, use the 2mm bullet connectors supplied with the motors. Don't forget to put the male bullets on the motor wires and the female on the ESC wires.