You need to measure either O2 or CO2 and CO. It is easy enough to measure temperature, then the efficiency can be calculated. Environmental monitors don't have a wide enough range, and so you have to use an emissions meter as used for boilers. These are expensive, and you have to pay to get them calibrated each year and have the cells replaced either every year for some types, or every two years for others. Price about £300 and calibration (annual) about £85.
Thank you for your reply, Roy. What would a calculation of efficiency look like? The weight or volume of the fuel in some relation to the temperature of the heater and then at the exhaust? ... I'm guessing here as you can probably tell. I'm just trying to get a handle on how much CO2 I would be adding to the atmosphere and if I can somehow sequester that much: aiming for net 0 carbon footprint.
Thew exhaust emissions are measured as a %age of CO2, or a %age of O2 as a proportion of the 21% of the normal atmospheric O2 level. Typically the CO2 would be in the range 8% to say 13%. The maximum possible is 15% but you have to have some excess air so that smoke is not produced. The efficiency is calculated from the excess air measured and the flue gas temperature. This is the combustion efficiency and is different from the overall efficiency which is feindishly difficult to measure anyway.
A couple of links for you. I work on oil boilers, and the measurements are a lot easier than for RMHs, but you will probably find them a bit taxing, I certainly do. Sequestering CO2 is best done by growing plants, like trees is a good example. Though I think it is good you have the attitude of trying to minimise the effect your activities have, don't try too hard with this from a combustion point of view unless you have enough land to grow the trees. You will never achieve a 0% carbon footprint. Even if you got anywhere near it for the wood heater, using a computer puts it straight out of the window, a gigabyte download uses over 7kWH!! that's a 1 bar electric fire for the working day.
A voice against shale gas fracking would be a far better gain than undue concerns about RMHs.