I was wondering if stock Android puts Wifi and other data networks to sleep when the display of the device is turned off. If not, what app can help me do the same ?
It depends, some Android devices have an advanced setting WiFi Sleep Policy under
Settings -> Wireless -> Wi-Fi Settings -> [Menu Button] Advanced -> Wi-Fi Sleep Policy
But I am not sure if this is a vanilla Android feature or an manufacturer modification. At least the Galaxy S series has this setting.
Data networks are usually fully active. But Apps like Tasker allow you to define certain profiles to improve battery life. For example: Only allow 2G when the display is off, because 2G requires less battery then 3G (UMTS).
I don't think it turns the WiFi or Data networks off. You can try by downloading an app from market and while it is downloading, turn off the screen. You can see that even after the screen is off, the download completes after some time. I am not sure exactly which app does this but you can try searching the market for such an app.