I am part of my college robotics team. We are participating in Robocon 2014 and are thinking about using mecanum wheels. We have done our research but one thing id like to clarify is: Does the number of rollers in the mecanum wheel effect its strafing? if yes then how?
No, the number of wheels does not affect its strafing. Strafing is affected only by the angle of the rollers relative to the wheels, and you shouldn't need to worry about that for standard mecanums. The reason for this is that as your robot moves (let's assume constant velocity), the wheels spin; as they spin, the same velocity is on a different part of the wheel, which continues to spin freely. No net effect, besides a minor bump, will occur from rolling a wheel forward.
Of course, everything with a limit. The number of rollers will affect the bumpiness of the movements. The more rollers, the less vibration your frame will undergo. Obviously, for instance, four rollers won't work. However, again, most commercial mecanums have at least enough for decent smoothness.