The Lumia 820 pops easily out of it's shell. Try removing the phone from the shell. Is there gunk in the power button of the case? You can clean the shell out with water or whatever, since there are no electronics in it. Just be sure that it is fully dry before assembling your phone again. If the phone shell is actually damaged and that is why the button is sticking, then you will probably have no choice but to buy a new shell.
If it's not gunked up on the case, then there may be something on the phone electronics. You can take a Q-tip, put some rubbing alcohol on the end of it and wipe the push button for the power button and get it wet enough to de-gunk the button, actuate the button a few times by hand or by pressing with the dry end of the Q-tip. Let the alcohol dry, it will only take 10 seconds or so for it to dry completely. Reassemble the phone and you should be back in business.