Stranded wire is great for electronics projects because it's durable and tends to be easier to solder to than solid core wire. However, if you've ever tried to use stranded wire in a breadboard or some other type of socket, you'll know what a pain it can be. Loose strands of wire may have even short circuited one of your projects before. Next time try coating the stranded wire with a little bit of solder to keep the ends sticking together.
Heat the stranded wire with a soldering iron and apply a small amount of solder. Use the soldering iron to spread the solder around the strands of wire until it evenly coats the exposed copper. Use a pair of wire cutters to remove any excess solder that may have accumulated on the end of the wire.
Now the stranded wire should fit into you breadboard with no problem.