> The jury's decision isn't final (and I thought this was ruled on by a judge directly, instead of a jury, but I could be wrong).
The idealized rule is that the jury is the final arbitrator of matters of fact, while judges (and appeal courts) decide matters of law. Ideals don't match reality cleanly, especially on matters like fair use which is "mixed fact and law." But additionally, you can sometimes appeal matters of fact by arguing that no reasonable jury could have reached the facts as it did (these are very rare, as I understand it, except in situations where mixed fact/law comes into play).
Some other points you're missing. First, you have to appeal on particular failures of law; you can't just appeal that you don't like the decision. In particular, if you try to appeal past the appeal court to a higher court, you can only make arguments that you made to the appeal court.
Another important thing is that appeal courts can push the case back down to the lower court to redecide based on clarifying law. That's what happened here, essentially. Google won on the trial, Oracle appealed saying that the judge incorrectly ruled that the API wasn't copyrightable (and the appeal court agreed with Oracle), which told the lower court to try it again with the correct ruling on API copyrightable. Google tried to appeal SCOTUS, who refused to hear it. Lower court had another jury trial, which found Google had fair use. Oracle appealed again to appeals court, which found that the jury couldn't have thought it fair use. Google appealed to SCOTUS, which just now disagreed with the appeal court.