Q:

What was the liquor that was based on petrol which was produced in the USSR during the Second World War?

I have a 1971 Spanish edition of the book "Stuka Pilot" by Hans-Ulrich Rudel where he recounts his memories of war. 
In the second chapter, in which he talks about the first combats of "Operation Barbarrossa" in 1941, there is a paragraph that seems to indicate that Soviet civilians used petrol to make homemade liquor. The following is my English translation:

For my part, I especially regret the petrol, 
  as the old women of the villages in
  the region exchange it for fresh eggs. Apparently, they make liquor
  with it. Naturally, this exchange is forbidden, but everyone loves
  boiled eggs. As for the liquor, which the villagers try to resell to
  us, it is a particularly infernal variety of rat poison, so strong
  that it is not possible to withstand one of its drops on the skin. On
  the other hand, the Russians drink it without a gesture.

I couldn't find more information about this ersatz homemade liqueur. What was it called by the Russians? How popular was it in the Soviet Union?

A:

There is quite some strange quotation mixing up the interpretation. My version of that book reads:

An ancient L.A.C. had been trying to fill his lighter from a large petrol tin. He does it by tilting the tin with the result that the petrol spills over the lighter whereupon he keeps flicking it to see if it is already working. There is a terrific bang; the tin explodes in his face and the L.A.C. pulls a face as if the explosion were a breach of military regulations. A sad waste of good petrol; for many old women are only too glad to swap eggs for a little petrol. This is of course forbidden, because petrol is meant for other uses than the concoction of spirituous liquor by old women. Even one drop of the stuff they manufacture burns our skin.
Hans Ulrich Rudel: "Stuka Pilot", Ballantine Books: New York, 1958, p24. (On archive.org: p. 34)

And this does not talk about any "drinking the petrol".
This is just a misconception. He is talking about gas, kerosene, that was used then to barter with the locals. The locals then would use this as fuel to burn, but not raw material or crucial ingredient or synonym for: to distill moonshine. Just for heating the still. This is most probably a type of vodka, like @sempaiscuba noticed called samogon.
Rudel, claiming to be a teetotaler, is of course opposed on these grounds alone to moonshining. Based on his inexperienced stomach for these kinds, it's no wonder that he disliked it.
But one thing remains, this is not liquor based on petrol, but ordinary grain or potato alcohol.
It was so popular that the highest Soviet outlawed it in 1948.
The Junkers Jumo engine for example used:

Junkers Jumo 210 – Fuel type: 87 octane rating gasoline
Cooling system: Liquid-cooled, ethylene glycol

One German version of this book reads "Eier" in at least two places:
p167: Almost all of a German Wehrmacht soldier's pay is invested in buying eggs. (Describing one situation, that he paints as 'excellent'.)
And the quote from above then reads:

Als er in Janowici zum ersten Mal zu uns ins Gruppenzelt kommt, ist gerade großer Lärm. Ein uralter Obergefreiter wollte sein Feuerzeug an einem großen Benzinfaß füllen. Um es gut zu machen neigte er das Faß und Benzin läuft über das Feuerzeug, woran er dauernd fleißig dreht, um zu sehen, ob es noch geht. Es tut einen unheimlichen Knall, das Faß  fliegt ihm um die Ohren und der Obergefreite zieht ein Gesicht, als ob das Faß gegen die militärischen Vorschriften geplatzt wäre. Schade um das Benzin, denn viele alte Frauen tauschen gern Benzin gegen Eier. Natürlich ist das verboten, weil das Benzin eine andere Bestimmung hat als die Branntweinerzeugung bei alten Weibern. Wir können davon auch noch nicht mal einen Tropfen auf der Haut vertragen. Alles ist eine Frage der Gewohnheit.
__When he comes to our group tent for the first time in Janowici, there is just a lot of noise. An age-old lance corporal wanted to fill his lighter at a big petrol barrel. To make it good, he tilted the barrel and gas runs over the lighter, which he keeps flicking to see if it's still possible. It makes an incredible bang, the barrel flies around his ears and the corporal pulls a face as if the barrel had burst in violation of military regulations. Too bad about the gasoline, because many old women like to exchange gasoline for eggs. Of course this is forbidden, because gasoline has a different purpose than the production of brandy by old women. We cannot even tolerate a drop of it on our skin. Everything is a question of habituation. (My translation)

As the gas (Benzin) the soldiers had access to would usually not contain any alcohol to begin with, distilling any of it would not be possible in these conditions. But Rudel seems to think at least that old women are in the habit of using it the process of manufacturing spirits (Branntwein).
That may be true, but is just his reasoning and not proof. He probably saw just what was exchanged, in this case gas, eggs and spirits; connecting some dots. For moonshining you just need any type of heat source. That he just declares this gas to be used just for moonshine anyway is another form of contempt he displays towards the locals.

