Is there any motor which moves slowly and gives strong torque?
The cheapest and most common thing you will find is a stepper motor. You can salvage a few of those from old printers and scanners. 
And if you use microstep control, you can make it very slow and accurate (below the fundamental step of the motor). The problem with steppter motors is that they consume lots of current regardless of speed.

In any case, there are gears that can take a lot of torque. The gearbox in your car does a good job, for instance.