So I decided I have enough of my modern rifles (plus at this point I'm pretty sure the writing is on the wall) so I'm starting to accumulate some lever guns.

I understand their designs, different action types, etc. but what I'm not sure about is the strength of particular styles.

I know the ones with the falling lugs are good, and strong designs. That's obvious given they come in magnum pistol calibers and full power rifle calibers.

I'm referring to the older style rifles. The 1866s and 73s.

From what I can tell the 66s are usually just 44-40 or 45 Colt, and the 73s add 357.

Are the 66s too weak to handle 357? Are the 73s strong enough to handle a steady diet of not nuclear loads, but loads strong enough to take out 4 legged creatures?

The 73 is a fine rifle/carbine for the caliber it was intended.  IMO it will not last long with .357 ammo.  It will likely out live you with black powder .44-40 or .38-40 loads.  It is quite powerful with those loads. too.

Word is that hot .357 will stretch a steel 73 frame.  A brass 66 frame would stretch even faster if it were available in that caliber.

If you want to shoot hot .357, shop for a 92.

I'm not trying to be smarmy, but after some googling, all I found is issues in .357 after a '73 has been modified with short stroke and SASS kits, where pins broke after the rifle was modified.

Is there a documented instance where the frame was stretched after shooting factory loaded .357 through a factory '73?  Or even shooting SAAMI-spec non+P .357 reloads through one?

I dont have much experience with the modern reproductions, but I have owned and shot many originals. The weakness in the 1866/1873 design is not the frame, its the bolt. The 1886/1892 series provided much better strength. Even original 1886s and 1892s will fire smokeless loads, something you would not dare do with an original 1873. I would think a steady diet of 357 in an 1873 design would not be a great idea. If you want a 357 rifle, I'd go with the 1892 design.

Yes there is, but you just do you.

The only reason I have .357 rounds is because they are hot.  I keep them out of my 73.

Can you post a link?  My google-fu is apparently lacking .  Again, not trying to be an antagonistic jerk, legitimately trying to learn.  The only issues I found were after short stroke kits were installed on 1873s or the rifle was otherwise modified (non-stock).  The 1866 issues seem obvious, due to brass receiver.

I thoroughly enjoy .357, and also enjoy older mechanisms (which to me are inherently fascinating), I'm just trying to learn more about the limitations of modern iterations.  (I even have a thread in this forum asking about a Spencer rifle reproduction in .357).  

If an 1873 doesn't handle .357 particularly well, that marks it off my list of Things I'd like to own

A manufacturer wouldn't release a gun if it couldn't handle the caliber it's chambered for.

I have a Winchester/Miroku 1873 in .357 Mag and I have no qualms about feeding it a steady diet of magnum loads. Modern metallurgy is leaps and bounds above 100+ years ago.

Perhaps, generally speaking, but SAAMI pressure levels for .45-70 are low for older trap door Springfields and their replicas.  So, there are now three different defined power levels for .45-70 with rifles and ammo loaded accordingly.  Most lever guns can handle higher pressure mid-level ammo, some lever guns and single shot guns can safely handle very hot Garrett and Buffalo Bore .45-70 ammo that is much more stout.

I would not recommend shooting Buffalo Bore 405 grain soft points at 2,000 fps from a trap door Springfield.  Nor does Buffalo Bore - very strong "no" from them.