Energy of a standing wave I've been taught that energy of a standing waves remains between the nodes of the wave or in other words energy remains within the wave. I wanted to know how that's possible.
Also if energy of a standing wave remains trapped within the wave, how can we hear the different harmonic sounds like a guitar or a flute?   
 A: There are multiple parts to your question.

energy of a standing waves remains between the nodes

When you look at the motion of a guitar string, it looks like this:

The part between the nodes is moving, while the nodes remain stationary. When the string is flat (and moving fast) all the (kinetic) energy is indeed between the nodes. However, when the string is fully stretched, the energy of the wave is stored in the elastic energy of the string - and it is in fact equally stored all along the string.
At that point, there is a vertical force experienced at the end of the string (the string is pulling up, and the support is pulling down). 

Where this string is attached to the sound board of the guitar, it will pull on the sound board. Moving the sound board up and down by a little bit changes the volume of the body of the guitar. The air is alternately pressurized and depressurised as the volume shrinks and grows. This results in pressure waves emanating from the guitar body (and in particular from the sound hole).
As this happens, the string is doing work on the sound board. Effectively, if you consider the standing wave to be the superposition of two traveling waves (one to the left and one to the right) then the motion of the support on the sound board results in imperfect reflection of the sound wave. The part that is not reflected is transmitted and becomes audible sound; the part that is reflected becomes part of a smaller standing wave, and so the amplitude of the string eventually decays.
If you look at an electric guitar, the "sound board" is typically a very solid piece of wood (or other material). By virtue of being so solid, it barely moves under the influence of the string. The string loses less energy per cycle and "rings" for much longer. The sound is picked up electrically - typically using a magnetic pickup that can sense the motion of the metal strings. This tiny electrical signal is then amplified so you get a lot of sound out of the string without the string giving up a lot of energy.
In summary, the answer to the last part of your question is this:
In a perfect resonator, there is no energy coupled from the resonator to the "rest of the world". Real instruments are deliberately designed to have a finite coupling of energy so that they can be heard; the consequence is that their sound will "die" when you stop strumming / picking / blowing etc.
A: Let's think about sound waves. Sound waves is a pressure wave ie it propagates by the change of pressure in the air. If you have a standing wave then the places where there is high pressure and the places where there is low pressure remains the same. You can compare this fact with a swinging string fixed at both ends. The reason why this happens is that the reflected wave and the incoming wave interfere in such a way that the superposition of them is a standing wave. You can find the mathematical description of a standing wave on Wikipedia.
The pressure waves coming from a musical instrument are not standing waves. If they were so you wouldn't hear them as you've said, because well.... they are just standing in their cavity. The musical instruments are designed such that the sound cavity lets some of the pressure waves out. They also make the sound louder and hence drain the energy of the string (eg for a guitar) faster but that is not relevant in this context. These wave travel in air and change the pressure at your ear drum, which results in the movement of your ear drum and hence you hearing the sound.
A: Energy transported by a standing wave gets thrown back by reflection.
-> Consider a standing wave thrown back by total reflection - no energy transport takes place.
A partly reflected wave sums up into a standing wave which gets overlapped by a running wave. In this case energy gets transported.
If you want to understand why a guitar works, I would recommend reading this article (among other things): http://en.wikipedia.org/wiki/Room_modes
