Interesting thread.
In my experience this a very grey area depending on aircraft type, bird type, nature of strike, and engineering support at destination.
Big bird, big strike on departure is a definite return in my book.
Small flocking birds .. Swifts and Starlings pose another problem altogether :
one may have taken an obvious hit but in fact suffered several.
All to often one is not even aware of a strike until the walk around prior to the next sector ... one dead swift hanging off a gear leg for example.
In this case a call or ACARS to engineering is a wise move : they can at least give guidance as to what needs looking at properly before departure, or better still arrange for a tame engineer to take a look.
On my type a small feathered friend going through an engine core is accompanied by an unmistakable stench through the air conditioning !
That case will always need looking at properly (Borascope) and that dictates where you go.
That's obviously just a rule of thumb, but I hope it contributes something to the discussion.
TR