Sounds like it needs major surgery rather than a prune Dilly!
You can cut them back but I think you'd need to seal the wounds with something like
Aborex compound to stop infection getting in. As to when, thats a toughy as you'll be cutting some pretty thick branches so it could "bleed" if you did it now or early spring (when sap is flowing).
Best I dea would be to get some electrical insulation tape & look at it now. Any dead or diseased branches mark with tape & and then do it in winter & take these out first. Then any branches that are damages (where they've rubbed together) & then any that are growing inwards. this should give you a nice open shape with loads of airflow. to help reduce disease. Don't forget to paint the cut surfaces with a sealant though otherwise disease wikk enter through the wounds.