I am not expert on tankers, but have some experience with level sensors.
The volume of liquid can be measured by a pressure sensor at the bottom, if the tank is continuously vented to the air. An absolute or gauge sensor can be used in this case, but the fuel vapour pressure needs to be accounted for if the tank is sealed - either two absolute sensors, one in the bottom and one in the vapour space, or a differential gauge (2 pressure ports). As these can be obtained with about 0.1% accuracy, that is the accuracy of the depth measurement. A variation is to bubble air in through a tube at the bottom of the tank, with the sensor "teed" into the air line. This helps keeps the sensor parts out of the liquid, as the sensor can be above and outside the tank. Such a sensor still needs all the parts like diaphragm and body to be able to work in the fuel because fuel and vapour may come back up the tube sometimes.
There are various other level sensors, chose one that has the accuracy to suit. These include types that sense the level at the surface (includes non contact). One such is an ultrasonic sensor as in the link below. The ultrasonic sensor looks down to measure the surface level through the vapour above the tank.
To detect leaks it may be possible to pressurise the tank slightly with air, say one or two KPa above the atmosphere, and measure the flow rate of the (constant) pressure source to the existing leaks/vents. If the flow changes there is a leak. This might work to some extent with a vented tank. Venting may be 16KPa, -2KPa and 30KPa. This is the equivalent of charging a capacitor from a voltage source through a resistor with a resistor bleeding the capacitor. The "normal leaks" need to be consistent.
It may be necessary to install some sensors in a larger vertical tube in the tank, to provide damping through small holes near the bottom so they are always covered. This averages out the variation due to liquid moving around in the tank. This is a filtering method, and equivalent to electrical filters, it can be made higher order.
With fuel it is necessary to use sensors designed to be intrinsically safe. The energy (electrical excitation) that is allowed to enter the sensor is less than that needed to ignite the fuel vapour. That way even if a short develops in the wires or during an accident (think of a sensor or wire being crushed) there is no issue from the sensor. I think it best to keep all that part external, using air as the pressure transfer medium.
Most sensors measure height/depth. This translates to volume in the tank through the shape of the tank, which has to be modelled in the calculation. A look-up table may suit, as there is only going to be 1000 points resolution or less. The fuel density (gm/l etc) may come into it if fuel is sold by weight. That needs a measure of temperature for corrections and a densitomer (specific gravity) reading. The volume changes about 0.1% per degree C for most liquid fuels. That may need temperature correction for greater accuracy, considering the sensor is able to show that change. The level varies as it sloshes around. Some sensors have averaging built in, or use a filter tube.
I included a link to a tanker access cover which shows the various relief pressures all combined in one fitting. Sensors are sometimes called transmitters, as they transmit information (by wire mostly).