You can create any amount of torque with your bare hands. Just pick a long enough lever. Archimedes famously said: "Give me a place to stand and with a lever I will move the whole world." (source: Wikiquote). Do note that Archimedes said nothing about the speed which he can move the whole world; he just said that he can in principle move the whole world.
However, the limitation here is power, not torque. The speed at which your hands or feet move is limited, and once you are operating near your maximum power, you may not be able to be as strong as you are when not moving at all.
Levers and gears can change the force or torque (the rotational equivalent of force), but none can change the power. The power is a fundamental thing that must come from an energy source.
There are two useful formulas: power is the rotational speed (in radians per second) times torque, or alternatively power is the linear speed times force. Levers work by modifying the speed and force in opposite directions; the end result is that their product is the same. Gears works similarly by modifying the rotational speed and torque in opposite directions; again, their product stays the same.
About torque levels: with a 170mm crank, a heavyweight strong bicyclist weighing 100 kg, pulling up with the rear shoe at 30 kg (and pushing up with the front shoe at an additional 30 kg), and pulling up from the handlebar at 25 kg, can reach 310 Nm: (100 kg + 30 kg + 30 kg + 25 kg) * 9.81 m/s^2 * 0.17 m = 308.52 Nm. Gears can multiply this: e.g. 22 tooth front gear and 32 tooth rear gear gives you 449 Nm. So, not only can you create torque more than 390 Nm with your bare hands, you can actually do so on a practical machine, a bicycle, with your feet.
But no way can a bicyclist produce 110 horsepower! A bicyclist is limited to about 1 horsepower in short bursts, and about one third to one half of a horsepower in longer durations.
So, how does a car engine differ from practical levers and bicycles powered by your hands or feet? It's the rotational rate! Car engines rotate so fast that no way could you produce such fast rotation with your hands or feet. The force and torque levels in car engines, however, are similar to what you can produce with your hands and feet in practical applications.