LOL you're a funny guy. OK seriously, there are some in Japan but I don't know of any in the USA. BTW, these are normally referred to as "series" or "classes" not leagues. You're best bet for some local competition is auto-crosses.
That looks like NASCAR identifying there car as Chevy, Toyota, etc. I don't think there is any part on those machines made by the manfacture.
Fine you win!! Here are some un modified Prius taking it it to the streets!! The track is where this type of recklessness really should be performed though!!
There's plenty of Toyota parts on that car. They're just not Prius parts. (Actually, I want to say that the battery is from the Prius α (the Japanese-market Prius v).) They're mostly parts that Toyota has developed specifically for motorsports over the years (the engine being derived from a 2003-2005 Indy Racing League engine).