Why do 100 nF ceramic disc capacitors from multiple sources, measured with two instruments, all appear to be below tolerance?
Perhaps you should buy one or two parts with known provenance, such as  a 100nF BFC241641004 +/-2% film cap from Vishay-Dale, which are less than $1.50 ea. 

Keep them in a cool dry place and never do anything with the capacitors but remove them from the storage location and measure with your instrument. 

To answer your question, there are/were some really horrible ceramic dielectrics such as Z5U and Y5V that age and and change with temperature greatly. Y5V will typically decrease in value by ~7%/decade hour after manufacture, so if those parts are 20-30 years old it's conceivable. Most modern parts use somewhat better dielectrics such as X7R in that capacitance range. Even class I (NP0) dielectric is available in values that high now. 

Also, if your cheap meters put a DC voltage across the capacitors that may decrease the value significantly. 

More likely there is some problem in your measurement technique, the meters are faulty, need a new battery or something of that ilk, but getting a single known-good reference would allow you to nail it down. 

If you feel like experimenting you can 'cook' your capacitors for a couple of hours at 150°C which would restore the aging, if it was aging. This won't do much for the solderability. 

Especially with the class III (Z5U/Y5V) caps, the tolerance applies only to the value 1000 hours after manufacture or 'cooking', at a reference temperature and with 0VDC applied across the capacitor. The value may have already decreased out of tolerance before you receive it from a distributor. Or it could be a bit out of tolerance high if it was shipped quickly.