"She has a day off today." (good sentence. It means she has taken a day off work) "She is having an off day." (means she's having a bad day) If you know that the person has, for example, got a whole week off and they are going on holiday, you could say: "She's on holiday." or "She's in France for the week."

various way [ she is out of the office / it is her day-off today / she is having a break from school or company / she is on a vacations / she took a day off ]

'He/She is away' is almost a direct substitution for 'He/She is off' They may be 'away/off' for holidays,sick leave,accrued work leave/leave with no pay, etc 'away off' is a casual term, but one you will hear all time.