No need to clear customs. The entire arrivals/departures area of Changi terminals are transit areas.

You can even catch a good night's sleep inside the transit area, at the Ambassador Transit Hotel: http://www.harilelahospitality.com/transit_hotel.html

Not aware of any 24/7 lounges, but there are plenty of places in the terminal that you could hang out overnight if you don't want to spend for a room. Maybe not the most comfortable places, though...