Your main problem is the human-friendly arrangement of the module. I'd say the "easiest" way is to rearrange the data in order to make it computer-friendly so a pivot table can read it. In a sheet of your choice, put in the specified cell the given formula/value:
Cell A1:
Sheet
as header of the sheet list.
Cell A2:
January
as the name of the sheet with the call logs of January
Cell A3:
February
as the name of the sheet with the call logs of February
Cell A4-A13:
you got it, type the rest of the call logs sheet name.
Cell D1:
Month
as header of the month list.
Cell D2:
=IF(D1="Month",INDEX(A:A,2),IF(COUNTIF(INDIRECT(D1&"!B:B"),"Call Number")*12>TRUNC((CELL("row",D2)-CELL("row",INDIRECT("E"&MAX(AGGREGATE(15,6,ROW(D$1:D1)*1/(D$1:D1=D1),1)-1,1))))/5-0.1,0)*12+1,D1,INDEX(A:A,MATCH(D1,A:A,0)+1)))
Cell E1:
Row
as header of the row list.
Cell E2:
=TRUNC(COUNTIF($D$1:D2,D2)/5-0.1)*12+1
Cell F1:
Call Number
as header of the call number list.
Cell F2:
=INDEX(INDIRECT(D2&"!"&"C2",FALSE),$E2+1)
Cell G1:
Date
as header of the date list.
Cell G2:
=INDEX(INDIRECT(D2&"!"&"C2",FALSE),$E2+5)
Cell H1:
Nature
as header of the nature list.
Cell H2:
=INDEX(INDIRECT(D2&"!"&"C5",FALSE),$E2)
Cell I1:
Off
as header of the officers list.
Cell I2:
=IF(INDEX(INDIRECT(D2&"!"&"C"&((CELL("row",I1)-CELL("row",I$1))/5-TRUNC((CELL("row",I1)-CELL("row",I$1))/5,0))*10+5,FALSE),$E2+2)="","",INDEX(INDIRECT(D2&"!"&"C"&((CELL("row",I1)-CELL("row",I$1))/5-TRUNC((CELL("row",I1)-CELL("row",I$1))/5,0))*10+5,FALSE),$E2+2))
Then select the range D2:I2 and drag it down to report its formulas until they returns errors. You should now have a computer-friendly list. You can use it as a source for a pivot table. I'd suggest to put: Nature in the filters; Off in columns; Month and Date in rows; counts of Call Number in values. Of course once you've pasted the formulas, you can move them from their positions. So if you want to put them in the Main sheet, just create the columns you need to place them in the correct addresses and then move them as you please.
Extra tip
I assume that you tend to manually report your data in the log; to accomplish that, you copy-paste-clear-compile an old log. Using VBA you could make this process faster, safer and you could also store the data in an already computer-friendly way while keeping the log format for the human interation. This way you wouldn't need all these formulas to rearrange the data.