It very much depends on the position you're applying for. You can't expect a one-size-fits-all answer here. Some companies are looking for someone who can get started right away, others are open to training their new hires. You need to find the job listings that are listed as entry-level.
For example, if I applied to a "Java developer" position, what kinds of skills might they expect of me?
I suspect you're thinking that a specific title has a specific skillset that you're required to have. That really isn't the case, especially for software development. When I apply for the same "C# developer" role, different companies use different technologies and give different importance/weight to certain technologies.
If you're looking for an entry-level job, there shouldn't be too many expectations on your proficiency with specific technologies, but the point still stands that there is no universally applicatble list of skills for a given job title.
I would suggest that you shift away from the "specific skills for a role" mindset, as it is often the willingness to adapt to different technologies that companies value. It's not just about what you know, it's about what you're willing to find out/learn.
Would an interviewer be looking for a good-enough knowledge of Java, or are there other factors?
It's usually not even that technology specific (though mileage may vary). I've applied for several positions where I didn't have specific experience with the technology the company used, but my experience with other tech stacks and willingness to learn were more than sufficient for a company to still make me an offer.
Don't just tell the interviewer you don't know how to do that, focus on telling them you're willing to learn. If you have equivalent experience in similar enough languages/techs, refer to that.
The skills of a developer is not just which syntax they know, it's the general skill of developing software (analysis, breaking down a problem, learning new concepts, keeping up with new releases) that is the main selling point of a developer.
If you showcase that skill, you'll vastly improve your chances to get an offer even if you don't know the specific language in question yet.
... whether it's possible to gain work as a software developer simply by building up independent knowledge in the field I'm applying for, without a CS degree
You don't need to have a degree in CS. I didn't have one but I found an employer willing to take me on. In my case, there is a government-sponsored employee training program that made it more attractive for companies to hire people without a degree or practical experience, but colleagues of mine have been similarly hired without a degree nor that sponsored program.
But I do strongly suggest that you build up a portfolio, enough that people can see you've got the aptitude for software development. Build a few simple applications and put them on a public repository, contribute to some open source projects, build a website, ...
Software development and IT in general is a field where a degree isn't a hard requirement (barring highly specialized roles, which "developer" isn't), and experience/aptitude are given significant weight as well. But in absence of a trusted certification like a degree, you're going to need to proactively demonstrate your experience/aptitude in order to be considered for the position.