How long do they usually keep someone sedated after a drug overdose?

Depends. Treatment of drug overdose varies greatly on the individual case. It depends on what drug the patient is detoxing from, how long they have used it, how high of doses they have used and any other complicating factors they may have such as chronic medical problems. The sedation is usually meant to help decrease the effects of withdrawl and may be needed for just a few days to a week or more.