Cost and effectiveness of different heating fuels
Here's a spreadsheet made available from the Maine State Government:
Some things in it are probably wrong, particularly prices, but you can fix that easily by plugging in the current fuel price where you are. The handy thing is that it gives BTU contents of a number of fuels per unit.
In order to compare apples to apples, you have to know how efficient your heater is, how much your fuel costs per unit, and how many BTUs per unit. For fuel oil (sadly common here in Maine) it's 139,000 BTU per gallon. Other fossil fuels are similarly easy to look up. For firewood, you can look up each species and get the BTU per cord, but you can bet it will be in the pretty close to 6400 BTU per pound. The BTUs per cord is proportional to the weight per cord. Since there are about six pounds in a gallon of oil, that makes oil a little over 3 1/2 times as energy dense per pound as wood. But there are plenty of places on line to look up the BTUs in a cord of Oak versus a cord of Fir. Remember though, this is for dry wood. If the wood is wet, all bets are off.
Combustion efficiency varies from about 10% for an open fireplace (or worse, depending...) to 50% for a barrel stove, to over 90% for a Russian style masonry stove or some kinds of rocket heater. Most oil furnaces are around 82%, give or take 5%. Pellet stoves are around 85%. Resistance electric heat is 100% efficient, but the power is often expensive. Air source heat pumps are around 300% efficient, but they don't work when it's very cold. Ground source heat pumps work when it's cold, but are prohibitively expensive to install.
So in the last column, you see what it would cost to heat the average house in Maine (at the time the spreadsheet was developed) with various fuels.
Because I heat with manufacturing waste wood blocks, my fuel is cheap. If you cut your own wood, try to put a dollar value on your time. I know that isn't easy to track, and sometimes the wood doesn't get measured well, making it hard to know what you've burned.
And then there's a value in knowing the source is reliably local, sustainable, not fossil carbon, etc...