Hi Katyan.. Yes it's true, it's very important to take a day off from strength training. When your muscles repair themselves, that is when they get bigger and stronger and healthier! By not allowing yourself that time, you are not getting the benefits you are working for.
That doesn't mean you can't exercise at all though! You could go for a walk or a swim or something like that... maybe don't push yourself as hard as on your workout days, but you can still move!

This might help you keep away from the foods that tempt you. Another thing you could do is split up your strength training so that you do some on one day and some the next--i.e. Arms, legs, abs/torso.
Also, coming to this forum is a great way to stay motivated! You might want to check out the "Chicks in Control" board.