Where is the boundary (if any) between oxymoron and paradox?

Dictionary definitions aren't wrong, but because of historical limitations (print on paper, publishing hard copies, and, for the internet, time in reading), definitions tend towards the most condensed version and letting the native speaker fill in the gaps. Often the definitions will miss nuances that are obvious to daily users of the terms.

Seeing a few examples, which dictionaries usually don't have, should distinguish them.

An oxymoron is a contradiction in terms, usually just two terms, usually an adjective and a noun that contradict each other. Some examples of oxymorons are 'jumbo shrimp', 'military intelligence', 'open secret'. They may be actual contradictions, or rely on multiple meanings, or simply humorous.

A paradox is a statement of a phenomenon that sounds impossible. It may turn out to actually be impossible or maybe actually possible. So it is a claim that can need a lot of description to get to the point where one realizes both what is expected, what actually happens, and how that might be a contradiction. Some examples of paradoxes are a catch-22, optical illusions, or hormesis.

So the difference is an oxymoron is a contradiction in terms, two words whose semantics are at odds, and a paradox is a situation which doesn't seem possible.

The phrase

Nobody is alone in being alone.

does seem to straddle both these ideas. On the one hand, it's saying 'everybody is together in being alone, together and alone being contradictory -terms-. But it also is a complex situation aside from the individual terms used where being solitary is a situation of individuals and it is possible that all individuals could share this situation, which is paradoxical.

So which is it? There's no law that says it must be one or the other and not both. And an oxymoron is easily considered to be a paradox in terms, as much as a contradiction is paradoxical.