It's a slang word among young people here.
Some students now talk to us just as if
they were talking to their close friends.
"Don't talk TAMEGO to your seniors."
'Even talk'? Is there any more slangish words
for this kind of talk?
Well, English isn't as strict as Japan about honorific of pecking orders. so I think your question is one of difficult one to understand without any explanation of culture. No all readers know well about Japanese custom, does them? :)
Anyway, I don't know why are you wanting slangs but can't you paraphrase with "polite/impolite"?
Something like "Don't talk impolitely to your seniors." or "I'll recommend to you to use formal language to your seniors.".
... While saying such, I'm not confident about my grammar. XD