Raspberries - what to do?

If the plants are vigorous, then the love where they are now so I'd not move them. They don't like transplanting much and it will set them back a few years to recover.  What you need to find out is whether they're summer fruiting or fall fruiting/everbearing. I imagine some neighbour plotters would recall when they saw berries on your plants.

for now, just cut out all dead and diseased canes, do any bit of weeding that you can, and spread loads of old muck around the bushes so they're ready for spring. By then you should know  what type you have and can prune accordingly. I wouldn't prune now as you might have summer fruiters which are on this years canes.