PBW = Powdered Brewers Wash. It's for cleaning beermaking equipment, but works on lots of other stuff, too - especially hard to clean rotisserie parts and grill grates. It's a tad expensive, but you only need a TB per gallon of hot water. While the rotisserie basket sticks out of a 5 gal bucket, it's easy just to flip it over after a couple of hours and soak the other end. And as Peqoud noted, it's magic! Just wipe down with a sponge or paper towel and rinse. No scrubbing at all.
If you can't get it where you live, or want to save some $$, as PBW is a bit pricey, you can mix up your own approximation:
Percentages are by weight. 75% Oxyclean 25% Red Devil TSP/90 (TSP=trisodium phosphate)