My three week old kitten is not using his back legs at all, they are spayed out to his sides and he is draging them when he moves - is this normal?

NO! Get to the vet straight away. Please, please please. It is not right, anything could have happened, during birth, or it may have been hurt or possibly it is just deformed. Whatever VET VET VET VET! Call now.

The thing that came to my mind is did your mama cat have kittens or did someone give you a 3 week old kitten? 3 weeks is much, much too young to be taken away from it's mother. All sorts of problems can occur from this. As colbtech states, please get your kitten to a vet as quickly as possible. Something is wrong.