Looking at the Jenkins interface this morning, I realized that I'd forgotten to give the anonymous user read access to jobs, so I've done that. I also tracked down the issue with the stylesheets to (I think) a permissions problem with the oXygen installation; it was installed via sudo, so all the files ended up owned by root, whereas the job is running under a different user. I've chowned everything to hcmc:hcmc, and we'll see if that solves it, but it might have to be chowned to whatever user Jenkins runs under. Running a stylesheet build now to see if it works.
EDIT: But it doesn't. The same error shows up even when java is world r-x. Posted on the oXygen forum for a possible solution, and also heard from SR that he remembers this but doesn't remember how he fixed it.