Translation:I sleep during the days and work during the nights.
Actually "I sleep during the day and work at night" is better English. The context would make it clear that this was habitual. The use of plurals sounds strange to my (native English-speaking) ear. You could say, rather colloquially, and maybe mostly in America - "I sleep days and work nights". But "during the days" just does not sound right....unless I am missing something?
I am guessing that it is because "during the night-time" only sounds like it happens once whereas "at night" sounds more habitual, yet "during the daytime" sounds more habitual. "In the daytime" is fine, too, and could be used for a habitual action or a one-off, but "at daytime" doesn't make sense in English.
Yes, I thought the question was specifically about the case with the. The closest translation of at night is på natten and to work nights is att arbeta natt in Swedish (this works like a particle verb), currently the former is accepted but not the latter. The main problem is probably that it's more natural to use the definite plural in Swedish than it is in English.