Help with creating a macro that will copy and paste data to multiple sheets.

Maybe this can get you started?

Sub harkin123()
Dim i As Long
For i = ActiveSheet.UsedRange.Rows.count To 2 Step -1
        Select Case Range("G" & i).Value
            Case Is = "NSSR"
            Range("G" & i).EntireRow.Copy Sheets("NSSR").Range("A" & Rows.count).End(3)(2)
            Case Is = "Req Brief", "Sponsor Approval", "Portfolio Board", "BTRD"
            Range("G" & i).EntireRow.Copy Sheets("Projects").Range("A" & Rows.count).End(3)(2)
        End Select
        Select Case Range("E" & i).Value
            Case Is = "Awaiting Functional Approval", "Awaiting Estimate", "Estimate", "Estimate Issued", "Budget Approved", "Active", "Rejected"
                Range("E" & i).EntireRow.Copy Sheets("NSSR").Range("A" & Rows.count).End(3)(2)
            Case Is = "Registered"
                Range("E" & i).EntireRow.Copy Sheets("Un-worked").Range("A" & Rows.count).End(3)(2)
            Case Is = "Registered", "NSSR", "Estimate", "Estimate Issued"
                Range("E" & i).EntireRow.Copy Sheets("Active Inbox").Range("A" & Rows.count).End(3)(2)
            Case Is = "Closed"
                Range("E" & i).EntireRow.Copy Sheets("Closed").Range("A" & Rows.count).End(3)(2)
         End Select
 If Month(Range("F" & i)) = Month(Now) Then
         Range("F" & i).EntireRow.Copy Sheets("Opened this Month").Range("A" & Rows.count).End(3)(2)
 End If
 Next i
End Sub

You would have too work on what should go on Sheet Active Inbox vrs what doesn't.