For example, a CFM56 is designed to be able to ingest birds...during testing actual dead birds are fed into an engine.
The CFM56 is most assuredly, absolutely NOT designed to ingest birds. It's tested for the effects of bird strikes against fan blade integrity. It is not designed for bird strikes, however.
A 737 also has a MUCH stronger multi-layer laminated windshield. While a 737 is going to hit a bird a heck of a lot faster than a 152, a bird could just as easily if not more easily penetrate the 152's windshield, or completely disable its engine that was never tested for a bird (most likely prop) strike.
What a 737 can or can't do is largely irrelevant.
When you talk about a bird disabling the engine on a 152, you're confused. When you compare it to a CFM56 you're also confused. Where tests have been conducted on turbofan engine fan blades, the birds were not fed into the engine itself, and the birds were not tested through the engine.
Bird strikes to the engine of the Cessna 152 are really meangless, as there's little means for a bird to be ingested into the engine. A bird passing through the propeller is really a non-event. Most of the time the bird doesn't survive the passage. The propeller, however does. Further, the stresses on a propeller blade traveling at 2,500 rpm are very different than those on a thin fan blade turning at 5000 or higher RPM.
In a worse-case scenario in which a bird manages to block the induction air inlet (bearing in mind that the induction in the 152 isn't easy to block, and comes with an alternate air source to rectify the situation, in the form of the carburetor air heat control), it's fixable. A bird isn't going to damage the cylinders or engine case. The engine installation in the Cessna 152, then, is entirely unlike that on a B737.
Examples of significant bird strikes:
Significant Bird Strikes to Aircraft
Debunking some myths surrounding bird strikes:
Bird Strike Committee USA
A Cessna 152 bird strike:
YouTube - Bird strike against cessna 152/ Impacto de ave. Argentina