Which of these three phrases below do you think is correct when someone asks for the day off from work? I've heard them all, but I think only one is correct.

Whichever one works best is the correct one.

I think the correct phrase is: "I need the day off on X-day." Calling in sick when you just want the day off would be wrong ;)

call in, sick

Called.  Reason?  SICK. 

The end.  There is no in nor out nor still nor off.

I came, I called, I vomited. 

"Called in sick" is the only one I hear around here. 

called in sick

Called in hungover.

In this day and age, the correct phrasing is, "Shut up peon, back to work!"

Sick days are only for Teh Magik Job Creatorz.

Yes, I'd say so :)

3

called-off-sick.

When someone asks for a day off from work it's usually in advance and it's called a personal day or a vacation day.  

When  someone is sick, they aren't generally ASKING for a day off.  They're telling the employer that they're taking the day off due to their sickness.  In that case, I'd have to say "George called IN sick today" (as in the boy made a telephone call IN to work to say he would be OFF work due his throwing up and acute diarrhea.