Every birdstrike is different.
Recovered a Harrier once where a seagull had entered the radome, then into the pressure bulkhead, coming to rest jamming the right rudder pedal. After about 10 days, when we arrived at the a/c, the significant remains were aromatic.
Hit a black back gull in a Rallye, dep Calais. Gull hit the engine fairing, dropped into the airflow, and then went between the slat and the wing.No damage, as such, but the gull was very much intact when we landed to check for damage.
There are so many factors involved here. I have seen plenty of dents, no damage as such, on commercial aircraft as an engineer, others, where the damage has been significant.
As for engine ingestion, you would be surprised just how many remains you find around the intake / first compressor stage.
What comes out of the back however, is not simply "ash"...for any bird that does make the full transit as it were, bits of engine invariably follow it out of the exhaust. I have also seen photographs of the subsequent deep strip of an engine, with bits of bird still visible at various stages of the engine.