if you draw a straight line between the avoider's center, and the obstacle's centers, then take the line from the avoider to it's destination, whichever side the line is on relative to the center line, is the side you should turn toward.

Shoot random rays in a cone ahead of you. 1 per frame. If it hits, immediately shoot another one straight forward. The orientation of the two points where the two rays hit (if the 2nd one hits at all) gives you a picture of whether the obstacle is angled toward or away from your immediate direction of travel. It also gives you an approximate angle that the object is oriented at. Therefore, you could choose to turn far enough to align parallel to the object (or farther).