Why does my sick dog goes outside and looks at the house?

It sounds like he is preparing to die. Dogs do odd things when they are dying. I have had dogs die from cancer and they would do the same thing,stare. If I were you,I would skip the oncologist. Trying to keep the dog alive for a few more weeks while giving him chemicals that will make him feel worse,or having him die at the vet all alone, is not a good idea. If he is not eating, then he is saying he feels very bad. It would be a kindness for you to just take him to the vet and hold him as he is euthanized. The chances of a dog being cured of liver cancer are astronomical. He is in pain, he is nauseous and he can't tell you,and so he stares. He is telling you with his eyes to let him go.