Can companies still use Java for free since it's now owned by Oracle?

Using Java is free. However, to use Java you need a JVM and to develop in Java you need a JDK. Oracle provides these for some platforms, but they allow the creation of the JVM and JDK by others subject to certain license terms. But you can't call the result Java without passing certain compatibility tests because they also own the trademark on the name Java. At issue in this case is, can you make a copy of the JVM and JDK from scratch without copying any of the original code and including the Java Class libraries, not call it Java and thus avoid any liability to Oracle (then Sun). Re-implementing from scratch could run afoul of patents, but the first case eliminated them as an obstacle. You could run into copyright problems if you copy the actual code, but in this case they did not (except a minor exception by accident in the Dalvik JVM, which had already been removed). If you don't call it Java, then there is no trademark issue. So, the only thing left is the API of the Java class libraries. You have to copy it is you want the same Java code to run on the original JVM and your new one. But there have been prior court cases that have ruled that the API is not copyrightable. On the other hand, in some instances the API is trivial, but designing a library framework clearly involves creative work. I think of it like this. Imagine any work of literature. Copying it is a violation of the copyright, except for the manner designated "fair use". What about copying the first letter of each sentence? They are random letters, not creativity, so it doesn't seem like it would be copyrightable. But what if the literature was also an acrostic, with the first letters spelling out sentences, essentially another work of literature embedding in the first, is copying the first letters a problem then? This is what the courts are deciding.

As mentions, it's more about modifying the VM and libraries, than using it as a platform for other programs. However, this brings on some questions, like here: As for whether companies pay Oracle to use Java, no they don't pay to use the Java SE , right now.

I haven't read the suit, but I would have to assume the suit is over the Dalvik VM.  Dalvik is Java "plug compatible" with Java source code but is based on none of Sun's Java VM technology. Sun (and now Oracle) always charged some segments of the market for Java, most tellingly J2ME on mobile phones.  For other markets, such as desktop, they have made Java openly available. I strongly suspect that this suit has to do with control over the VM and its deployment rather than its use once deployed. Note that I Am Not A Lawyer.  Furthermore, I have no visibility into Larry Ellison's head.... thank god.

I think the issue is about creating programs and running them for free. AFAIK, any java program you create (class files, jar files) can run for free on any JVM, proprietary or not. If you create JVM's that may be a different story.