"Jordbær" can indeed mean strawberry or strawberries, but here it's clear that it's strawberries. As for how we know: strawberry is a countable noun, so if it were singular, it'd have to say "a strawberry" or "the strawberry" (et jordbær / jordbæret). It doesn't, so we can know it's plural.
So the only way it could be considered correct to translate it as "I eat strawberry" is if it's not referring to the actual fruit, but some other (uncountable) substance. For example, in England the red sugary stuff that people have on ice-creams tends to be called simply "raspberry", and works in sentences such as "Would you like raspberry on that?" - we don't have a substance that's just called "strawberry", but if we did, that'd be the way to justify the sentence.
"de" = "they" (generally speaking)
"-en", "-et", "-a", "-ene" = "the"
"de" can appear as "the", but only in double-definite plural forms, ie those recognisable by them having an adjective ending in "-e" and then a plural noun ending in "-ene", as for example "de røde jordbærene" ("the red strawberries").
Yes, this does mean that "Do they eat the red strawberries?" would be translated "Spiser de de røde jordbærene?", but this is no stranger than the English "The drugs that he had had had had no effect on his driving" ;)
So this sentence would actually be literally translated "eat they strawberries?" (of course this construction sounds strange in modern English, having gone out of fashion nearly five hundred years ago - hence the given "Do they eat strawberries?", which is more natural these days).
Your translation, "Eat the strawberries?", would (for what it's worth as a strange-sounding phrase in either language, but that could be justified by context, such as checking one heard correctly, for example) be translated "Spiser jordbærene?"
On a tangential note, "De" (capitalized even if mid-sentence) can also mean "you" in polite old-fashioned Norwegian, but you'll not see that much, and these days people think of it as pretty much Danish.
Anyway, it's late and I'm tired and that causes me to have odd responses like spilling random trivia about the exciting topic that is the word "the", so I'll shut up and go to bed now ;)