What could cause lifter-like noise in an OHC engine?

2005 Ford CVPI 4.6L Modular V8 178k miles, but based on the fact that there is a sticker on the engine, it’s probably not the original one. Check engine light is on but I can’t get the codes because it won’t connect. I used a BlueDriver on Android and iOS as well as two different standalone scanners that my neighbor has (just fyi that I didn’t use some cheap pos scanner).

I bought the car from the city of Hemet, CA, through a government auction site for $1400. When I picked up the car their mechanics said it was parked because of a misfire. They pulled the whole engine out and couldn’t figure it out so they put it back in and so all the seals are new. They claim however the car was not making the loud noises when they parked it; it only had the misfire. They think it’s just from sitting and said it was lifter noise but it’s overhead cam engine: it doesn’t have lifters. It quiets down significantly after a minute or two but still doesn’t sound right. It’s puffing white smoke and smells horrendous. Could a head gasket cause this noise? If it’s not a head gasket, what else could it be?

And not sure if it’s related to the issue but about a month after I got it home and basically just parked it, it also started to leak a sizable amount of oil, only when running, coming from somewhere on the passenger side bank on the exhaust side. Haven’t been able to do a leak dye test yet, but I’ve heard those engines are known for blowing valve cover gaskets. (I would like to reiterate that my question still pertains to the engine noise; I just threw in the oil leak because I don’t know if it’s relevant. I know you guys don’t like a laundry list )

Sorry this is kinda long. I really would like to get this car running again because I think it’s really cool as it has a whole lot of the police stuff on it still.