I've never read or watched Those Who Hunt Elves, so I'm leaning heavily on Wikipedia and Archen's Anime Page.
According to Archen's Anime Page, there turns out, by a shocking coincidence, to be some kind of nut available in the medieval fantasy world that can be turned into gasoline. (Scroll down to where it says "T-74" under "Characters".) That seems to be what keeps the tank moving for the first bit of the manga.
In both the anime and manga, the tank is at some point possessed by a cat spirit named Miké, as stated on Wikipedia under "Mihke". According to Archen's Anime Page, this happens earlier in the anime than it does in the manga. It seems that the cat spirit can move the tank without needing any fuel—Archen's Anime Page says under "About the Manga" that "the T-74 was still at the bottom of the river, until Miké's spirit moved into the tank and drove out of the water." This TV Tropes page also implies that the tank actually did run out of gas in the anime and couldn't move until it was possessed by Miké.
It's not very clear from my sources, but it seems the gasoline nut was just a stopgap to keep the tank going until the mangaka came up with the idea to have the tank possessed by a cat spirit, and the anime writers decided to just have the fuel last until the cat spirit came along. (This is supported by the Wikipedia description of Episode 5: "Ritsuko's tank runs out of fuel in a town terrorized by the spirit of a deceased cat which can possess inanimate objects.")