The two station car parks are, as Maidup states, open 24 hours per day. A single day's parking fee covers you from 0400 one day to 0400 the next day, so overnight parking requires you to pay for two days.
The 24-hour period starting at 0400 on a Saturday is charged at £4.00. The next 24-hour parking period is charged at £2.00. So you'll have to pay £6.00 for your overnight parking.
While Stevenage Station car park probably fills up very quickly during the week, I doubt that you'd have any difficulties finding a space on a Saturday. (I used to run a railway station on a commuter route into London, so I've got some direct knowledge in this area). There are 123 spaces on the south side and 330 spaces on the North side.
Source:
http://www.nationalra...ions/svg/details.html
Chris