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The units for torque, as you stated, are Newton-meters. Although this is algebraically the same units as Joules, Joules are generally not appropriate units for torque.
In physics, how much torque you exert on an object depends on two things: the force you exert, F; and the lever arm. Also called the moment arm, the lever arm is the perpendicular distance from the pivot point to the point at which you exert your force and is related to the distance from the axis, r, by.