I believe that all the Sony MC50 variations have the same camera body and all of them should fit the HD Wave housing.
The variations are for different markets. MC50U is meant for U.S.,whilst MC50E (I own one) is for Europe. The differences relate to different frame rates and the external power supply. I do not know about MC50P. Sounds like PAL(?), but, why would there be a parallel MC50E version?
The Aquatica/Amphibico HD Wave housing is compatible with Sony HXR-MC50, Sony XR550 and CX550. Apart from difference of the external microphone, decorations on the side of the camera and some differences in the menus (i.e. features included/excluded), these are basically the same camera. The XR550 and CX550 are lower priced than MC50.
Do not confuse this older HD Wave housing with a slightly newer version with the same name. The newer version is meant for Sony HDR CX560/700 cameras.