eat out means eat at a restaurant, not at home (e.g. There wasn't anything to eat at home, so we decided to eat out. We couldn't be bothered to cook so that we ate out last night.)

eat up means eat all of something or consume, to take away a large part of something (e.g. If you don't eat up your breakfast, you can’t go anywhere. My big old car eats up petrol.)

end up means in result, to finally be in a particular place or situation (e.g. They're travelling across Europe and ended up going to Turkey.)