I tap threads in wood using (self made) roll taps. For me, that works better than using taps, single point threading on the lathe or thread milling. The drill diameter depends a bit on the hardness of the wood. MDF is predrilled using the drill diameter for steel, hard wood (oak) is drilled using the drill diameter for roll taps.
If you don’t have a roll tap, use a hex bolt to check the quality of the thread. A bolt gives the “same” result, a roll tap just takes less force to make the thread.
I don’t make outer threads in wood, but measuring the thread size should be as easy as measuring the thread size in steel using the 3 wire method. You don’t need a calibrated wire, just 3 straight wires (nails) of known and equal thickness.