In excel, dates are just numbers. Days, specifically. Fractional parts provide time of day. For instance, today, May 19, 2014, is 41778.
Put each date range into two columns, side by side, one range per row:
5/1/2014 5/18/2014
5/3/2014 5/24/2014
5/12/2014 5/15/2014
5/7/2014 6/30/2014
etc
Now if they all overlap at least a little bit, then the highest date in the left column will be lower than the lowest date in the right column.
So you can use max() and min() to find out:
=max(A1:A4) =min(B1:B4)
This will return two numbers. You can format the cells as dates to get the dates they represent.
If the max is smaller than or equal to the min, then all the ranges overlap by at least one day (inclusive). If not, then there's one or more ranges which do not overlap the rest of the group. You can sort by the left and right columns to find out the max and min that cause a problem, if there is one.
If there is overlap, then you do end up with the date range in the max/min calculations.
If the ranges include time (fractional part of the number) then it will still work correctly and give you an exact timeframe for overlap.
