Strength is defined as the maximum amount of weight one can move through a dynamic activity (through a range of motion). This is not the same as peak force, which can be measured isometrically (with no movement through a range of motion).
Power is defined as either force x velocity (displacement/time) or work (force x displacement) / time. The key factor in power is the time factor, which is why it is such an important variable for real world tasks and thus so physiologically relevant for human movement. There are even good data showing a solid link between muscular power and mortality in certain populations, so this is not just an athletic or human performance issue.
Training for strength can and will improve power, given the force aspect of the equation. In fact, there is more room for growth on the force side of the power equation than the velocity side, for most people. There is a reason that the most powerful athletes in the world also tend to be some of the strongest. Having said that, most persons who are really interested in improving their power don't only do heavy lifting, but also do movements which involve moderate and high velocities, such as ballistic movements or the Olympic lifts and their derivatives. However, you will never (or you shouldn't) see them doing only this, as it would ignore the fact that force makes up 50% of the power equation. Watch an Olympic lifter or sprinter train sometime, and you will see that they spend a good deal of their time lifting heavy.
Technique is not a power issue in that it increases or decreases it directly. However, having the correct technique for a particular movement might allow for the expression of that power compared to a movement where one is unskilled.
