In such case the Company that cause the delay is responsible Means you should head to a service desk in London and get a Paper/Zero Fare ticket to travel on the next day. According European Law that is still recognised by “National Rail” they even have to provide you with a possibility to stay overnight if you have to. Usually they provide Hotel Voucher or book a Hotel for you.

That should be possible. You don't get an extra inbound day but you just travel on whatever journey you had planned. A strike is like any other unexpected disturbance (when you had planned your journey before the strike was announced) and normal passenger rights apply, e.g. the right to continue your journey with the next available train(s) to your destination without any extra costs or the right to assistance if you get stranded.