How to measure total stair rise with uneven floor?
(For anyone looking at the history, I think I misunderstood the question to mean "what should I measure" and not "how should I measure".)


Geometry 


You can measure the exact length of the diagonal (a string from bottom front of first step to 2nd floor landing). Measure the angle of the string to the (assuming it is level) landing. Imagine the total rise and total run as the other 2 sides of a right triangle. Since you now know the 3 angles and the length of the hypotenuse, you can calculate the lengths of the rise and run. The fact that the intersection of the (virtual) rise and run may be above or (in your case) below the actual first floor is irrelevant.


Measurement


If there is a constant slope (not necessarily even but all one direction) then measure 2nd floor landing to first floor. Then place a long straight piece of lumber on the floor from the spot beneath the landing to the location of the first step. Shim it until it is level. Then measure the height of the shimmed gap between the lumber and the first step location. If the high spot is between the two key locations, simply add an equal amount to both - e.g., put a scrap 2x4 under each end, get it level and still add just the amount of the shims on the lower end, since you would just subtract the same extra piece on both ends it doesn't count at all.