Based on this (How are numerical bonuses combined?) question and its answer, the order is what would decide the effect.
Thus, if you were pushing/lifting over your normal carrying capacity and then haste was cast on you, your speed would be 10ft/round. (5*2=10)
But if you were not encumbered, haste was cast on you, and then you started pushing or lifting more than your normal carrying capacity your speed would be 5ft/round. (Normal speed * 2, then set to 5ft)
As a DM, I am not very fond of this methodology and I would enforce a consistent calculation mechanic. Something like: apply new calculation method (set to 5ft/round) apply all multiplicative (*2 from haste), then all additive (+10 ft/round from lets say longstrider).
So being under the effects of haste and longstrider and encumbered would always make your speed 20ft/round. (5*2+10=20) Not RAW, but I think it is pretty fair and easier to use than trying to work with order of operations.