For example in this phrase:
I translate it into "he might have some stories", but I have the impression it has many other meanings.
ネタ is a semi-slang term that comes from reversing the characters of "seed" タネ. It's a word with many uses, but in all uses it denotes the "seed" of the idea of a work, it's essential core.
In cooking, the ネタ of a dish is the key ingredient that makes a particular dish interesting. For example, the ネタ of a piece of sushi is the non-rice part of the sushi.
In a magic trick, the ネタ of a trick is the actual trickery that makes the illusion work (the part that Penn and Teller reveal).
In a joke, the ネタ is the core subject and punchline, before you pad them out with a story.
In news articles, the ネタ is the raw fact being reported (e.g. "oil rig explodes") before being fleshed out with prose.
In your example of 「話すネタ」, ネタ means topic of conversation.
ネタ alone is a bit vague: "stories", but usually in the sense of jokes or funny anecdotes. I'd say it has some connotation of "dirty" (or at least slightly off-colour) jokes/anecdotes, but that's more a matter of usage than intrinsic meaning.
ネタ is most often encountered in these two expressions:
下ネタ【しもねた】(or 下のネタ): lit. "jokes about down below", i.e. "dirty jokes"
You can probably encounter it in other expressions, where it carries the meaning of "joke". E.g.:
いい加減パンツネタはやめとけよな → Quit with the panty jokes!
In your example, I would translate it by "He seems to have some funny stories" or "good stories" etc.