First, "hypoid" refers to the kind of gear, not a kind of oil. It this case, it would be the pinion & ring gears in the differential. Hypoid gear oil is oil formulated for use with hypoid gears. It has an additive package that can handle the extreme pressure that these gears can create.
Chances are you already have hypoid gear oil installed in your diff (see above)
. Anyway, as a first step to solving your problem it would probably be advisable to change the oil in the differential. You may be running a bit low, or it may just be time to do it. Alldata specifies 85W-90,90 GL-5(Gear Oil, API Service GL-5). If it quiets down, then the problem is solved (for a while at least). Ultimately though, the whining is caused by a misalignment of the gear teeth. This can be caused by wear or bad assembly. Either way, the the only way to permanently fix it will be to rebuild or replace the differential.
My previous car (SLK320) had a slight whine in the differential for 50,000+ miles and never caused any problems. I found it was a lot cheaper to just turn up the stereo a bit.
