Oh boy an oil thread!
Clean oil is the best, change it regularly.
Any brand name oil will be fine in a stock 327,dino 5W30 or maybe a little heavier if you are in a hot climate area changed every 3K miles or syn every 5K if she's not a leaker or oil burner. Old Chevys do tend to leak so keep an eye on it, that's the most important thing.

 

 

 

You don't really need anything like that, just change it as needed and don't run it low. 327s are great engines ,some of the best of their time for sure.
I run diesel oil in my old 1974 Harley but it's an iron air cooled engine and gets damn hot,service manual says run 60 weight but it's pretty hard to find these days and the Delo diesel oil works pretty well for that kind of engine. My modern Harley gets 20/50 syn. and my LS1 Camaro gets Mobil 1.

Most likely valve covers are leaking and it's running down on the exhaust.
Valve cover gaskets are easy to change, the main thing is to get both surfaces really clean and dry then just a thin layer of silicone sealant and let it tack up a bit before installation, don't over tighten them especially the cork gaskets, just snug them down and do it again after a few heat cycles but don't crush them. I like to get both surfaces shinny metal with no trace of the old sealant or gasket material and then before applying sealant a quick wipe down with alcohol to remove any trace of oil, it evaporates quickly and leaves a clean dry surface . I've found it easiest to do the valve covers first with sealant and stick the gaskets to the covers, then put silicone on the gasket to head surface (on the gaskets)and set them in place after it tacks up a bit and bolt them down. They will go a long time without leaking if you take your time and do it right.

 

You want a zinc (ZDDP) additive oil with a flat tappet cam. The miles and condition will determine your viscosity..Maybe a 10w40 conventional oil. Like Y2K says about the rear oil leak hitting the exhaust is probably valve cover gaskets. Wouldn't hurt to check the oil sending unit behind the distributor for leaks also.

 

I had a Nova that leaked from the sending unit behind the distributer and it smoked really bad,the unit was old and the plastic had shrunk so it was actually coming out of the unit itself. New one and problem solved.
The ZDDP thing is debatable ,many say it's only needed for break in or engines with big cams and heavy duty valve springs but it certainly can't hurt. I've been running modern oils in my old '78 pickup with a big block 454 for 15 years and it still runs strong as ever.
I got this from another site posted by an engine builder.
"
This sorta thing is my game since I build a lot of old-school engines.
When it comes to flat tappet cams and lifters, they wear together. The cam and base of the lifters are both surface hardened, but not very deep. They start out with a specific texture and as they break in they wear each other to a new, broken-in texture. This is why you can't put new lifters on an old cam or vice versa. Think of it like this. Let's say you take two pieces of identical emery cloth and start rubbing them together. They would eventually knock the majority of the abrasive off and you can rub them together for a very long time once they've established even wear with each other. Now switch out one of the pieces of emery cloth for a brand new one. It will shred the worn-in one very quickly.
The lobes of the cam (and the lifters) are only hardened on the surface, so you can also picture them like a hard-boiled egg. Once you break through the shell, the stuff underneath is soft.
ZDDP is preferred for break in. The Zinc and Phosphorus compounds are anti-wear agents and the way they work is to increase the film strength of the oil so more stays in between the two components during valve actuation. Very important for break-in, not very critical once its broken in. If you have a flat-tappet engine that is already broken in, losing ZDDP won't really cause any headaches unless you were really close to wiping a cam before the switch. In that case, ZDDP would have only given you a few more months anyway.
The loss of ZDDP in oil hasn't shown to increase wear appreciably in direct contact engine parts. Suffice it to say that other advances in lube technology have all but closed the gap left by the loss of ZDDP.
The other thing of note is that with the obsolescence of flat-tappet systems, most lifter and cam manufacturers no longer make quality parts. As of a few years ago, I couldn't find a single lifter manufactured anywhere but China. Not that they couldn't make quality stuff, but Chinese metallurgy is still not up to par with what it needs to be, especially when many Chinese companies are still in the business of making things as cheaply as possible.
So, if you're breaking in a new cam/lifters, I strongly suggest using an additive for the first few thousand. If it's already broken in, use your favorite brand of plain old oil and don't fret it."

 

ZDDP is an anti scuffing agent for flat tappets. The flat tappet lifter is also keeping the cam from moving forward (cam walk). As the oil gets dirty and acidic, the ZDDP keeping the scuffing to a minimum. Also get a magnetic drain plug.