I need to replace the seatpost and the handlebar stem on my 1977 Schwinn Varsity but I don't know the diameter of either. Anyone know what size I may need on these two parts. Thanks in advance!

Regardless of the measurements, I highly recommend investing in a micrometer. I bought a digital unit at Harbor Freight for about $15. Their cheap plastic analog one is about $2. You will need one sooner or later.

Good first choice when you have a question.
https://www.sheldonbrown.com/seatpost-sizes-m-z.html

i do not recall the stem size.I believe the seat post is .833" usually listed as 13/16".

All of the Schwinn electroforged frames since '65 use a 13/16" seatpost and stem. The stems are more commonly called 21.1mm. 13/16" = .83" = 21.1mm.

Prior to '65 they used the same seatpost but a larger 7/8" stem.

The 13/16ths seatpost is a relatively uncommon size. They aren't difficult to find, but the ones you do find are usually steel. If you find a source of aluminum seatposts, post a note. I'm looking for one for my Varsity!

You might want a 'Wald #940' (10" length) or 'Wald #945' (15" length). Steel. These have the Schwinn diameter for the seat tube and the modern diameter for the saddle clamp:

https://www.bikepartsusa.com/bikepart...ategory=search

https://www.bikepartsusa.com/bikepart...ategory=search

The pictures in the bikepartsusa catalog are inaccurate. Much better: download the Wald catalog --
https://waldsports.com/index.cfm/guides-downloads.html. I've ordered them from bikepartsusa and they look like the pictures in the Wald catalog, not the bikepartsusa pictures.

To re-emphasize: Your Schwinn saddle clamp with the narrow hole won't fit with this. The typical-size modern saddle clamps will fit.