.packlist, Socket.bs, Socket.dll, I don't see Socket.xs.dll

The files you're seeing are not from Strawberry 5.24. They are part of a much older version.
".bs" files are no longer installed, and Strawberry now builds ".xs.dll" files instead of ".dll".

Your problem will go away if you remove that Socket installation (in its entirety) from perl/site/lib.
That will enable perl/lib/Socket.pm (which shipped with Strawberry) to be loaded - and all should work fine.

However, it's likely that there are other extensions from the older perl present in perl/site/lib.
Removing everything from the perl/site/lib folder is a valid option.
That folder is normally empty when perl is installed - the only modules that go into it are the ones that you subsequently install (or, as in your case, the files that were there from a previous installation :-)

Cheers,
Rob