I assume by "change layers" you mean toggling between invisible and visible layers. First you have to have the layer on your map as a Dynamic layer. Second every layer you want to change between must be in the service.
Then just create your check event for the radio buttons. In that event you can connect to your service layer which will have a VisibleLayers property which is an integer list of all the visible layers. Set only the ones you want.
Good Luck