This can be achieved with a simple preprocessor macro:
#define readEE(VAR) VAR = readEEPROM(AT24C32_ADDRESS, 1, VAR ## Pos)
You can then use:
readEE(foo);
and it will be expanded out to:
foo = readEEPROM(AT24C32_ADDRESS, 1, fooPos);
The ## operator in macros expands out both sides (VAR and Pos) and then concatenates the results together. Since VAR itself is a macro (whatever you pass when you call the macro) it gets replaced with that value, but Pos, because it isn't a macro, just stays as Pos. So you end up with your variable name concatenated with the word Pos.
Note that you can't use that in a loop with variable names in an array - simply because variable names only exist in the source code, not in the compiled code, so you can't do anything with those variable names once the code is compiled. Hence you have to use the preprocessor to do the job.
Yes, it means you still have to write 120 lines of code for all 120 variables, but they are just shortened to readEE(varname);.