maybe I am missing something but if the temperature during the test does not change ..and its not likely to unless the vessel is in the sun and filled overnight and can heat up with the sun enough to heat the oil which would not be easy, then the effect of temperature change on the oil can be ignored. The density for determination of the static head can be estimated from the SG of the oil at whatever temp is gets put into the vessel.
Dont see that compressibility is a drama.. oil is used more on hydraulic systems under pressure than water. using oil (fuel oil, diesel etc) on systems which cannot be contaminated with oil is common practice..AYBEE