hey there! PLEASE dont simply bury an extension cord! They are not designed for direct burial. You will need to buy wire designed for this or run underground conduit pipe and run the wire thru that. Always seal off the connections with some type of sealant.
2nd, if you cover the IR led's with electrical tape, you are blocking the light that they produce, therefore you wont have night vision anymore.
A birdhouse is a very good spot to hide a camera. Just dont kick any tenants out of there just to put a camera in it! I take it you want the camera to be covert, so be creative as to where to put em. Just keep in mind the IR's will emit that red glow, so if your trying to be slick, they'll give away the location. I know they sell IR cameras that dont emit a red glow at all, but they are more expensive
They have a wavelength in the 900's i think