Removing a deck need some real help! It's not that old and the wood is nice we want to reuse it but.....?
Answers:
I would try a forstner bit and if that does not work Sears sells a tool for removing broken screws. It drills hole around the screw so that the board will pop right off supposedly. Having never used it , I can not say for sure if it works which is why I would use a forstner bit. If you have never used a forstner bit , here is how it works , it bores a flat bottom hole. This means if you are good or real careful you can bore the wood away from the screw head and then use a screw driver to remove the screws. You should also be aware that if you are using pressure treated wood , you need to protect yourself from the carcinogens in the wood.Most important would be a face mask to stop the dust that you will not see , alas it will be there.
Other answers:
Try going at them with a sawzall between the deck boards and the supporting joists.
Try going at them with a sawzall between the deck boards and the supporting joists.
a sawsall will work great as oldmoose said,, you may also want to use a screw out set,, you drill a hole in the head of the screw and then use one of the scewouts with a drill in reverse to unscrew those messed up screws,, you can do this first or after you remove the boards with the sawsall.. they also have a new tool that you hammer one end on the screw or nail,, it will make a ring around the screw or nail that you then use the other end to pry out the nail or a small locking pliers to grab the screw and unscrew it..