Those female header connectors on a Arduino are not really designed to hold round wire well. A .025" square pin is what there are designed to work with like the pins sticking up on the ISP connector.
One thing you can do is buy some strip pins (break away headers) and break them off to single pins and solder them to the end of your hook-up wires. The long in goes into the Arduino connectors and the short end could be soldered to you wire.
Lefty