Translation:The interpreter speaks neither Swedish nor English.
Eller means or.
Heller means "also" or "in addition" but is only used in combination with a negating word, such as inte/not, aldrig/never, knappast/barely...
Tolken talar inte svenska. Han talar inte heller engelska. The interpreter doesn't speak Swedish. He also doesn't speak English.
Varken jag eller min kompis gillar fisk. Neither me nor my friend likes fish.
Jag tycker inte om fisk. Inte min kompis heller. I don't like fish. Neither does my friend.
Jag äter aldrig kött eller fisk. I never eat meat or fish.
Jag äter aldrig kött och inte fisk heller. Jag never eat meat and i also never eat fish.
Yup, but that's for when there is no "nor" part. Also, the neuter ingetdera is normally better since Swedish defaults to that in isolation.
- We eat neither = Vi äter ingetdera
- We eat neither a nor b = Vi äter varken a eller b
It's approaching formality, though, and you're not very likely to hear it in colloquial speech.
Sorry, but you're wrong – the traditionally accepted combinations are neither-nor and either-or. Today, many native speakers mix them up, but those are the two that traditional grammar recommends. It's not a double negation, because neither and nor do not negate the same thing, neither negates 'Swedish', and nor negates 'English'.