@MLE_online just for reference: my "energy efficient" refrigerator uses 40 Watts if running and runs 1/4th of the time so it ends up at an average of 10 Watts. So if its really the fridge depending on the price per kWh a new one could make financial sense within 1 or 2 years.
I found out that my washing machine draws 5 Watts constantly just for being plugged in and "off" so half of the fridge!
You could just try to unplug all devices that are not in use for one period/month and check how the value changes. This includes the Internet modem/router if not at home. If you have access to the meter just do it for 1 or 2 days and extrapolate the difference in reading to one month. This should give a good idea about wasted "standby" energy.
A used kill-a-watt should not be too expensive, maybe 20 bucks? You could sell it again after the investigation.
Is a small PV setup (e.g. one 400 W PV module plus a microinverter) an option for you?