How to secure flimsy wires from RGB LED strip in Arduino Uno breadboard?
If you really want to avoid soldering, you can use terminal blocks like these to connect stranded wires to a breadboard...



They are cheap and widely available. 

Alternately, you also just get some ~22 gauge solid (non-stranded) wire or breadboard jumper wire, strip one end and twist the stranded lead onto it. Cover the joint with some electrical tape, and you now have something with a nice end to stick into the breadboard.