I spotted a plastic piece, of some sort, inside my oil filter housing. It is about 1' square and has a little plastic nub on one side. Does anyone recognize it as anything? I'm trying to figure out what it is and why it was there.

 

I could be wrong but I think it once was a soft hose clamp. I saw the same broken piece on mine.

 

There is, or was on your car, a 'U' shaped support for the radiator hose that is held in that pocket on the oil filter fitting. Yours was broken off and the part that went into the pocket was left behind. You should replace it to prevent the hose from rubbing on anything and cause a leak.