Using Row & Column References in Cell Formulas?

I feel like I'm going crazy because I can't even find a Google search which answers this question...

Is it possible to use R1C1 type references to other cells within cell formulas? Something like "=SUM(R1C5:R4C5)" instead of "=SUM(E1:E4)"?

I would like to reference values in a certain row and column depending on a date. Basically, I have a calendar at the top of a spreadsheet which shows the current month. On another sheet, I have a row for each month, with separate ones for each year (i.e. there's a row for January 2014 and a separate row for January 2015 twelve rows later) and columns for the days. In the month-day row-column cell is information on whether that day is a holiday (e.g. row 9 column 8 contains information for September 8, 2014). I would like for the calendar on the main sheet to be able to reference this row during September and the next row during October by subtracting the current month by the original month and using that value as the row number. The value in this cell would be the basis for conditional formatting, but it's not so easy using the address references like "H8" compared to "R9C8."

Thanks for any advice!

Thanks for the advice. The INDEX function was exactly what I was looking for in this case.