「避ける」は、自分にとって望ましくない事柄(状況・行為・対象物など)の存在をあらかじめ知っていて、それとの接触、かかわりを持たずにすませる意。
避ける means you avoid something or someone. (You already know bad thing will happen to you so you prepare to avoid it )
ex, Is she coming to the party?? I am not going because I don't want to meet her!!
I have been avoiding her since last time we met.
(彼女を避ける)
ex 2, I will stay little bit more I want to avoid traffic jam...
(交通渋滞を避ける)
「よける」は、主に対象物との物理的接触から、自分が動くことによって逃げる意。また、「邪魔だからわきによけておく」のように、物を移動させる意もある。
よける is more like... you move from something or you move thing because it is on your way.
ex. In front of you there is a puddle, you walk around the puddle. (avoid the puddle)
Your movement is よける。
水溜りをよけて歩く。
I hope my explanation help you a little.