The airline would put me on the earliest flight next morning, but do I get compensated for the night's stay.
In the EU you have a right to accommodation and food if your flight is delayed by more than 4 hours. That includes being bumped from a flight. There are some narrow exceptions, but in general if your flight starts or ends in the EU then you are entitled to this support and additional monetary compensation.
This website has extensive details of the rules and your rights.
It depends on your itinerary. If you are just starting your flights for that leg they would likely do nothing on the assumption you will just go home and return in the morning.
If you are enroute from A to C and get bumped at your stopover at B, then they would most likely provide you with accommodations and perhaps meal vouchers (though meal vouchers rarely cover a decent meal at the hotel's restaurant).
This also depends a bit on why you are being bumped. If it is not the airline's fault (weather related issue, etc) they might not do anything in either situation.