As of Nov 2019, the Oracle vs. Google case has reached the Supreme Court. Oracle is in the driver's seat, having won at Federal appeals court level. In reading through various articles, it looks like the core issue is whether you exactly copy the API in order to offer a competing product, i.e. one that users can swap out with your competitor and not have to change anything. If you're not doing that you should be Ok.
Sun made Java open source many years ago, but the Java use license prevents redistribution (as noted here). Unfortunately for Google, that's what they do: redistribute in order to compete with the copyright owner, without paying. IMHO, they will not be able to convince 5 conservative justices that this is ok.