A 1978 YZ80 is most certainly a YZ80E. The first YZ80 to feature a monoshock rear end. The frame and engine numbers should start with 2J5 for a 1978 YZ80.
Although there is good compatability between 1978 to 1980 YZ and GT80 engines, the 1979 YZ80F is probably the closest relative albeit with a 6 speed gearbox rather than the 5 speed. Cylinder, crank clutch and engine cases are basically the same and if they do not have the identical part number, I can tell you that they will still interchange with no drama.
Breaking the engine down is a simple affair, be methodical and take lots of pics to aide re-assembley. I have 2 spare engines here for parts if you find your in need of replacements or need pics of what goes where.
I would be tipping that the gearbox is going to be OK, I have pulled 3 crusty old engines apart and have found all of the gear boxes to be good, so not much seems to go wrong there.
The clutch outer basket is usually grooved in the thrust side of the fingers and would be possible to bring back with a careful dressing with the file. The clutch actuator mechanism usually suffers some wear and tear and would benefit from a good clean and regrease if nothing else, but you can probably count on buying a new plastic helix.
The left side magneto cover/ sprocket cover (intermediate casing) usually cops a beating from the chain flying off and thrashing the case. The case also servs as part of the clutch actuator housing, so there can be dramas getting a good case if yours is trashed.
The crank Big End and Main engine bearings are usually in need of replacing on these engines. Main bearings are cheap and easy to replace and probably should be done as a matter of course. Do the seals as well - goes without saying.
The big end should be inspected and replaced as an on condition basis. This job is best left to the machine shop if you have not got the proper gear to do the job. Parts are available individually or as a kit genuine from Yamaha (I bought a complete NOS crank assy from Ebay for $100 recently so keep an eye out for that sort of deal).
Source your part numbers from a site such as Partzilla in the USA, this will also aide in determining which parts are common to different models and will be very useful to see what parts might be missing or incorrect.
Airboxes are tough to find for these bikes for some reason, but any airbox from 1978 yz80 to 1980 YZ80 will fit and are identical despite the part number change. You are lucky if you have a good airbox.
DC Plastics make decent fitting side covers for the YZ80E. No one makes seat foams for them yet, but will by about March 17. Covers are available from Ebay. Spokes are available NOS pretty cheap and the front 16 inch rim is readily replaced with a 17 inch from a later model as the front hub is the same unit used on all drum brake YZ80s since the dawn of time, Back wheel is the same up to 1979.
Frames are weak on the 1978 YZ80 and a a factory gusset kit was available to weld in as a mod, the frame was redesigned for 1979 and is a big improvement straight up.
Throttle control cables are hard to find and there is not an aftermarket, fit a 1982 or later YZ80 throttle assembley and cable for a worth while upgrade (you will need to buy a separate kill switch as the original has the kill switch incorporated into the right side grip assy).
The rest of the controls are straight forward and easy to get from Yamaha or Ebay for chump change.
If your forks are not rusty then you are one of the few that does not have to re chrome or otherwise up grade to later model forks - not much advice for that problem, either option is not cheap.
Do yourself a favour and dont spend too much time trying to save the carby if the chrome on the slide is worn through to brass anywhere, grab a Chinese copy for $30 delivered and put your own jets and throttle cable mount in to suit.
I think that about covers it, good luck. The YZ 80E is a cool little bike.