Your parents have done a great job with your dog so far. First of all, he's lived to be eleven, which is a good, old age for an Akita. They've obviously treated him very well all these years. I'm sure that you've played with him, fed him, and helped take care of him, too. They did a good thing having the ultrasound done, and now they know exactly what is wrong with him. And y'all know now that you can't fix this, but can help him as long as possible.
A dog that is in pain will usually not want to eat anything -- and dogs with liver problems are nauseated and don't want to eat. You could try warming up some canned food and hand feeding him. Sometimes sick dogs would like that. To help him get around, you can sling a long towel underneath his lower belly to help him up and outside. Once out on the ground, he will probably do okay to walk around. Stairs would not be good for him now.
You can help by lying on the floor next to him and petting him and talking to him. Bring his water to him so he won't have to get up and down.
Your vet does have pain medicines like tramadol that he can gvie your dog. I'm sure it your parents call, they'll let you just pick up the medicine. They also have anti-nausea shots, such as cerenia that will help with stomach upset.
Sometimes when a dog is so tired and sick and weak, we believe that it's the final act of kindness to stop the suffering. You should talk about all this with your parents. They sound like some pretty awesome pet owners to me.
Your dog will let you know when he is too tired to go on. Your vet can also help a lot. Our vets won't tell people when to put their dog to sleep, but they will say something like "I wouldn't argue with you if that is your decision" when they bring it up. A good vet won't put a dog down unless he has to in order to stop suffering.
As far as the actual procedure goes, ask to have your dog sedated first. We give a quick shot in the hip that allows pets to fall peacefully asleep. It's the same med we use for surgery, and it's called telazol. Within 5 minutes, the dog has fallen asleep in his owner's arms. We later give a second injection that actuallly stops the heart. I have had to help with this many times, and while it's extremely sad, the dogs are peaceful in the end, right where they want to be -- in their owner's arms. We will go to the house to put a dog to sleep so it doesn't have to walk into the vet's office.
I honestly believe that whatever your parents decide will be the very best thing for your friend. They've proven that to me, because they were willing to go the extra mile with fluids and tests. It will be a very sad time for all of you, but try to focus on all the good memories, and soon you'll find them replacing the sadness. See if you can make a paw print (you can get the clay at a store like Michael's or Hobby Lobby) and find a really nice photograph of him in better times. You can frame the paw print and also have a canvas or enlargement of your friend's photo for your wall.
I have lost two dogs to cancer, and it is just awful. I do understand.
Take good care,