A question that I am not sure how to even ask...

yes, I have seen engines clogged in this fashion, more than a few, early Chevy's mostly.

If you put the oil in the engine, it is not leaking, or pouring out the tail pipe, not registering on the stick and the oil light is on. There really is no where else it could be.

I would jack up the back of the car to get the oil going in one direction, pull the valve cover and clear the obstruction clean/rod/ scrape it out trying to minimize what goes back in the engine.
After you get the heavy stuff out. There are engine flushes, gunk makes one, And some shops have a machine that can do it with a chemical. I have mixed feelings about this, but haven't had bad experiences using this equipment either.