Hole and pad size standard for wires soldered in through holes
A general rule of thumb would be to make your hole diameter (after plating) approximately 10% larger than the diameter of your wire. However, this will often lead to very small diameter differences. For example, 18AWG 16/30 stranded wire has a diameter of 0.046 inches (1.17mm). This value +10% gives you about 1.29mm, which is a difference of 0.12mm. 

Generally your best bet is to twist the end of the stranded wire to help prevent it from unraveling. You can increase the hole size to an extent, but it depends on your application, plating, type of wire, solder, current, etc. how much you can increase it before you run into issues. Personally I probably wouldn't go beyond 20%.