"I cannot talk to you either" = "non posso parlare nemmeno a te";
"I cannot even talk to you" = "non ti posso nemmeno parlare";
the two Italian sentences seems the similar, but they have very different meanings.
explanation: "nemmeno", "neppure" and "neanche" can be adverbs (=not even) or conjunctions (=neither/not either). they are adverbs when they're nearer the verb, they're conjunctions when they're nearer nouns and complements.
other examples: "non ci conosciamo nemmeno" = we don't even know each other - "nemmeno io lo voglio" = neither I want it - "Io non lo voglio nemmeno" = I don't even want it.
I hope to be understandable.
No difference. Neppure is slightly higher register and the other two more common in conversation.