Fit a gas meter on the line to the furnace? Would need a plumber of course.

For the electricity, a clip on CT (along with voltage) should be able to do what you need as long as the CT is placed after everything else but before your consuming devices. Needs to go only on one leg. I presume it's big enough that it's not a standard outlet.

I have this running on a Raspberry Pi (with a 14 channels of CT). I only have 7 CTs all running the main load at the moment and it's well within the rated accuracy of the utility supplied meter (i.e. <1% error). Can log pretty much anything it can measure at any frequency and has fully customisable dashboards. See https://openenergymonitor.org/ . It can be done fairly safely too with low voltage isolated measurement of the voltage and only a clip on CT.

There are other devices that try to "guess" based on the main load only. i.e. it knows the fan is a 1000W fairly resistive load so if it sees a jump in the main consumption of about that amount, it attributes it to the fan. A lot of assumptions and two loads nearly the same could not be differentiated. e.g. http://www.smappee.com/be_en/energy-monitor-home

If it runs on a separate circuit in you switchboard, you may be able to fit a DIN rail meter and just take manual readings too.