Torque is a force that tends to cause a rotation. A force applied at a non-zero distance from an object's centre will tend to rotate the object.
Mathematically, work is a force times a distance, and has units such as foot-pounds or Newton-metres. The direction of force (or at least a component of it) must match the direction of motion for the force to be considered to be doing work.
Torque is the cross product of the radius (or arm) and the force applied. A cross product is the product of a scalar, a vector, and the sine of the smallest positive angle between them which returns a vector. You can apply an infinite force at an incident angle whose sine is 0 and generate no torque...thus why you can't fire a cylinder at TDC.
Work is the dot product of force and distance. A dot product is the product of a force, the distance throughout which that force acts and the cosine
of the smallest positive angle between the two which returns a scalar. You can have a force working at an angle with or against the direction that force is acting and still perform work. It just can't be perpindicular (cosine of pi/2 is 0)
oh, also, the correct units for torque are Newton-meters not pound-feet. I look forward to the day when the non-metric units lay down and die.