How can a conductivity experiment have higher voltage than battery?
A voltmeter is a zero current(i.e. very high resistance) device. Therefore in your scheme, the readings you are getting are not reliable. The way to make that measurement is by either switching your multimeter into an ammeter in the configuration you have and measure the current, or adding a resistor to the circuit in place of where you have the multimeter now and connect the multimeter in parallel to that resistor. In either case, you will be measuring the current going through the solution, which will tell you about the conductivity.