I've read Murakami's 1Q84, and there are several problems with the English translation. We say turnoff, not turnout.
The Esso sign is a big billboard on top of a building at the turnout (turnoff). It would have been on the left side of the road as the oncoming lanes would be to the right (as you said) but since the building was behind the oncoming lanes there must have been distance involved and the road could have curved.
One sign, on top of the building, near the turnoff.
At least, that is how I interpreted it.