Need a formula whereby three conditions are met to return a result.
For example, If A10 and A20 and A30, then F1+F2. If A1<0 and A20
and A30, then F1+F3, etc.

There are 8 possibilities, if my understanding of the problem is correect.

One approach is to start with the formula below. It returns a text string
for each of the possibilities, showing which ones of the three input values
are positive.

=CHOOSE((N(A1)0)+2*(N(A2)0)+4*(N(A3)0)+1,
"none","A1","A2","A1&A2","A3","A1&A3","A2&A3","all ")

For your problem, you would replace each of the text strings with the
corresponding formula.

In this formula, input cells containing text are considered "not 0";
likewise for empty cells and logical FALSE. Dates are considered "0";
likewise for logical TRUE. If that's not what's required, adjust
accordingly.

Also, the requirements seem vague for when input value(s) are exactly zero,
so adjust the formula based on what's wanted in those cases.