You can take a taxi from the airport to Shanghai railway station to take train to Nanjing. Taxi fare may be around CNY200 at night. Well, you can also take the airport shuttle bus night line to downtown area and then catch a taxi to the train station. The train ticket is CNY141/soft aleeper and CNY101/hard sleeper. One things to mention, the night trains are temporary added during the peak transport time of the Spring festival.That means there are no trains usualy when you get to the railway station after midnight.
Then I advise you to stay overnight in Shanghai and then take bullet train to Nanjing the next early morning.