Re: "Don't use strength!"
At least you can recognize what is probably holding you back. People who are used to using their muscles often have a difficult time in not using arm muscles. I suggest practicing fully relaxing, being "dead weight." Try to relax as much as possible so you are difficult to move. Think of some actions where you need to use your entire body, such as pushing a car or tug of war. This way, you can remember the feeling.
Have someone hold your arm, and just relax it and let it drop. See your fingers relax and your arm will become heavier. It seems to me that when someone's fingers are tense their body is tense also.
My Sensei was having us become really tired at a seminar and told us that when people are tired their muscles relax and their throws improve. The trick is to notice when things ARE working so your body can remember that. At home you can practice consciously relaxing muscles, and noticing when you are doing similar motions to your goal. Maybe you are thinking of Aikido as fighting? Remember, you don't want to make your opponent fight back so they should not feel they are being fought with. You will see a big improvement in your technique with this change. Good luck on your test!