No compensation. A bird strike is an extraordinary circumstance.
Check your flightA bird strike is outside the airline's control and counts as an extraordinary circumstance, so compensation is not payable. The Court of Justice confirmed this in Peskova, which also confirmed that the safety inspection afterwards is part of the same event.
There is an important limit the same judgment set. The airline must still take all reasonable measures to limit the disruption. If a bird strike caused a one hour delay but the airline turned it into an eight hour delay through slow handling or by failing to re-route you on another carrier, the portion of delay it could have avoided may still be claimable.
As always, duty of care applies regardless. Meals, drinks, and a hotel if you are held overnight are owed even when compensation is not.
Compensation is a flat amount set by distance, not by ticket price: €250 up to 1,500 km, €400 for longer flights inside the EU and for 1,500–3,500 km, and €600 beyond 3,500 km. The UK equivalents are £220, £350 and £520.
Distance is measured in a straight line from your original departure airport to your final destination, which on a connecting itinerary often lands you in a higher band than you would expect.
Duty of care is separate from compensation and does not depend on the cause. Once you are delayed two hours or more the airline owes you meals and drinks, two phone calls, and a hotel plus transfers if you are stuck overnight. This applies in bad weather, during ATC strikes, and in every other situation where no compensation is payable.
Airlines frequently provide none of this during major disruption. Buy your own, keep every receipt, and claim the cost back afterwards.
Work out what you are owed