There are probably better ways of doing this, but not knowing why you have your sheets set up the way they are, I suggest the most direct and easiest solution. For each row in each sheet, you could have an equation like

=IF(E2=1,SUM(A2: D2),0)

and then you would need to sum this column in each sheet and sum each of those results.

Alternatively, you could have one equation for each sheet like:

=sumif(E2:E6,1,A2:A6)+sumif(E2:E6,1,B2:B6)+sumif(E 2:E6,1,C2:C6)+sumif(E2:E6,1,D2: D6)

and then sum those results for each month.

Or even combine the equations for each sheet into a single equation though as the number of calculated cells decrease, the equation complexity increases.

Or you could redesign your sheets. Why not have all the data on a single sheet with the additional field for Month?



PS...the emoticons are annoying. First I have noticed it.