Should I use a Dual 4-channel analog multiplexer/demultiplexer for powering up 4 sensors and getting their readings?
Yes, you could use half the chip to select the analog signal and half to control the power, provided the sensors are powered from Vcc, which must be 5V or less (5.5V abs max). 

For example, use 4x P-channel MOSFETs with gate-to-source resistors and ground the common so only one is on at once.







simulate this circuit &ndash; Schematic created using CircuitLab

If your sensors require a higher voltage then the circuit will have to be somewhat more complex, but the same chip can be used.