There is no drain plug as you know, although I tap one in the all the vette diff's I build.
You will need to get a suction gun and suck out the oil from the fill plug on the LH side. This is a square head 3/4" npt plug. Once you get it out, add 2 bottles of the current GM limited slip additive and top it off with standard gear oil- I use Lucas 85-140 gear oil but you can use any quality 90 wt gear oil. Synthetic gear oils are not needed. I know many will disagree but I have never used it in any diff I built and never had a problem. The additive is critical so use just the GM product - even though some oil claim to have additive in them.
Now you should know some things to check for. The 73-79 diffs had some issues that if left unchecked can leave you with a broken diff.
1- Posi chatter is common to all the Eaton spring loaded posi's, going back to 1965 up to '79 and the aftermarket. Most times the fluid change will resolve it. Do figure 8's in a empty parking lot to work the oil/additive into the clutches when side loading them. If this doesn't resolve the chatter you will have to pull the diff or live with it.
2- Axle endplay. The axles faces on the 73-79's were soft, they ride up against the posi cross shaft which is hardened. The constant rubbing wears the axles away and creates excessive axle endplay. If left unrepaired the axles will continue to wear until they crash into the axle seal boss and then the housing ears. I have had plenty shipped to me where this happened, some were rebuildable and others were junk. Get your car in the air and look to see how much endplay you have and if there is still a 1/8" lip at the axle seals. The noise you hear may be axles hitting the diff.
3- These diff's also have lousy clutches and ring gear bolts.
Now if the diff have been worked on or rebuilt since 1978 maybe these have been addressed. If the diff is original and untouched then you should take a close look.
You can contact me with any questions if you like.