I doubt you'll be able to calibrate or standardize your calipers. You need to know how far off they are at what size. Is it linear? Does it get worse as the jaws open? How close are the inside and outside jaws?
Ideally, you'd use gage blocks (also nicknamed "joe blocks") to verify accuracy. These are machined and polished blocks of various sizes. A set costs hundreds to thousands of dollars. If you have a friend who works at a factory with a metrology dept, you might be able to work out a 15 minute appointment to verify your calibration.
If it were me, and I didn't have access to gage blocks, I'd go to Tractor Supply or a big box hardware store. Look for "drill rod", or "polished and ground" steel stock. You can measure this and compare the advertised size with your results. Likewise, measure drill bit shanks and compare. If you have three pieces of stock, sandwich one between the other two and measure using the inside jaws. It is typical to get different readings between inside and outside jaws.
Also use feeler gages and, when all else fails,
coins .
You say your $10 electronic calipers measure to THREE decimal places? Mine only measure to 2. This really limits their usefulness.
Significant digits: it depends on your calipers' output. If the last digit indexes by 0.001, then it should be good to 1/1000". If it rolls from 2.031 to 2.062, then you are only reading to the nearest 1/32" (0.03125" or more likely 0.031".) It wouldn't surprise me if it read 2.030 > 2.035 > 2.040 etc., the nearest 0.005". You get what you pay for, oftentimes less.
Bill