I agree - is your father able to decide? Does he enjoy his life as it is now? My dad had had 2strokes his mobility, communication, lifestyle and everything were severely affected he did NOT want to live his life like that! Can he walk? Talk to be understood? Is he completely dependent on others for daily basic needs? Does he have a DNR? as someone who has fought oral cancer (radiation is brutal.. Chemo.. Not fun...surgery will be hard as well) and someone who has cared for a parent who was compromised severely by a stroke - I would personally say - think very carefully before going through with this treatment. Do your best to keep him comfortable and pain free and possibly let the disease play out its course. The reality is this. He is already compromised immune wise (history of long term illness, stroke, and already being in an institute). His health is poor - (does he have diabetes?) the chemo will cause major issues with his immune system, the radiation will burn him and prevent him from being able to eat and taste, short term at the least he will likely need parental nutrition, long term in the worst case scenario - this will require a peg permanently.
Now as a child watching a parent suffer it's the worst. If I could have done anything to save my dad I would have, but he wanted to die, (without a cancer dx hanging over his head) and he was only in the hospital/ nursing home for 10 mos. I cannot imagine that life for an extended period of time, then to take a man who is already compromised and throw this treatment into the works...
If he is of sound mind and able to communicate his wants ask if not personally I wouldn't go through with anything other than palliative care. It's a heart wrenching decision but you have to ask yourself why am I doing his? For him? For me? Hugs - it's not an easy decision ..

Ps - though it may sound from above that I am a negative Nellie..I have to assure you I'm not. I Am the opposite in fact- I am very much one of those people who tends to tell people to push right to the end. I think what has me worried here is your dad's quality of life. From the sounds of it your father has been incapacitated enough from the age of 50 (very young) to be living in a nursing home, to me that says he is unable to do most or all of his basic care. Chances are he has a lot of other issues (my dad was physically and mentally affected - strokes do have different effects based on locations so I can only guess as to his situation - if you combine this with a stage 4 dx I think it it may be more harmful than helpful to put him through treatment.