The contradictions in relation between current and voltage with regards to power and impedence
Depends on the type of load.  If all your loads are resistive, then the current will decrease with the voltage.  However, not all loads are resistive.  Your computer power supply, for example, is most likely a complex switching power supply that is set up to efficiently convert a high voltage, low current supply into a low voltage, high current output.  Assuming your computer requires a constant current and voltage, decreasing the input voltage to the power supply will certainly result in an increase in current draw.  The impedance of the power supply is most certainly not as simple as Z=R+jwL.  

It's hard to say exactly what might happen to the current draw of a whole house if the voltage droops.  It depends on what loads are turned on - it could either increase or decrease depending on how much load is constant impedance and how much is constant power.