As most people have stated, most "tube overdrive" is nothing more than snakeoil. So I am wondering: what is the minimum voltage a 12AX7 needed in order for it to be a truly overdriven preamp? (If I am not mistaken, the highest anode voltage is 300 volt, but usually is at 250 DC)

Also, EHX use a 12v/1 amp transformer for their English Muff'n; did they actually convert the voltage again within the unit?

Also, how is a tube preamp differ from a tube OD pedal?
Ibanez SA-120 (ed.2006)
BluesJr 1996-B + cathode follower + texas Heat
Crate CPB150
Homemade 4 x 10 cab Bass closeback
Metal Muff
There will be a big gap between pedals running the tubes in starvation mode and ones with full plate voltage, I would think. You're either running at 18V or 200+. Keep in mind that starvation mode when properly designed can be useful.
The muff'n does indeed have an internal transformer that ramps the voltage up to something like 275V. I can't remember if that's the exact number, I haven't opened mine in a while. But it is plenty.
A tube preamp and a tube OD pedal are pretty much the same thing. A preamp is really just a low-gain (in terms of volume increase, not distortion) signal amplifier, so anything that boosts volume can be a preamp if you want it to be. Hendrix famously used a fuzz face as a preamp on purple haze; "Black Dog" by led zeppelin uses two studio compressors as a preamp for the guitar part.