Motor dies after startup.

Is the oil smell coming from the exhaust or the engine compartment? Does the engine smooth out if you drive it or stay rough? The audio was distorted; good idea but the phone's vocoder will distort sounds like that.

How old is the gas? You say that the car has not been driven much for 5 years. If the gas, or any significant portion of it, is regular and is over 6 months old, then this is very suspect. Modern gas is VERY prone to do this. (Premium will do this to a lesser degree, so I am told.) It can do damage inside the engine. Even mixing new gas with old gas will not solve this; the varnish is already formed.

Get some gas out of the fuel pump and smell it; if it is good then it will smell like fresh gas at the gas station. If any of it is bad, it will have a distinct acrid smell of what I would describe as 'dog piss' . If you get any hint of that odor, the gas needs to be dumped 100% and the fuel system cleaned form tank to carb. Your carb's passages may be all gummed up now (which would explain why the fiddling with the mixtures screws changed things), and you can read good info in this forum about valves sticking due to varnish from old gas in the intakes, which can bend pushrods. (And it does not do the rings any good either, as it can cause detonation.) All the symptoms you describe can be casued by this. (The 'oil' small may be this too.)