Where's the common sense in presuming the aircraft has only two engines, or that a bird strike has taken out half of the engines, or that an immediate re-land is required?
From the multitude of bird strikes I've experienced, it is rare to know one has gone through the engine, most have been found on the post flight inspection.
The only written guidance I have is that after a bird strike, an engineering clearance is required. In the absence of any indications that an engine may have suffered damage, my inclination is to continue to destination IF engineering assistance is available and IF after assessing all the information I have, I deem it prudent to do so.