Using Indirect Function in SumIF?

I have one data sheet (SheetA), from which 340 other sheets are
populated. However within those 340 other sheets the data is
manipulated using various if functions to return various values. I now
want to take the outcome of those various functions - and put them in
a summary table.

Essentially to simplify: Data sheet A is manipulated on Sheet B, and
the manipulated data needs to be summarized on Sheet C.

I've tried using the sumif function, but doesn't return proper values
because the cells it is referencing are in-turn referencing other
cells on the original data sheet. I know in theory that the "indirect"
function is meant to solve this problem - but how would I use indirect
in a sumif or vlookup function?

Thanks!