Mail keeps message data in a folder, and mail account settings in a .plist file.
Supposing you know how to access the user's Library folder, you need to:
Copy the Mail folder (located in
~/Library/Preferences/) from the old Mac to the new one.
Copy the following file from the old Mac to the new one:
Mountain Lion or newer:
The procedure works best if you haven't tried to open Mail before. In case you did, as you try and copy the configuration file or document folder, OS X will ask you if you want to keep the old file, the new one or both.
About calendars (and notes and contacts, and possibly Chrome bookmarks), I'd suggest syncing via iCloud and Google respectively. The offline procedures are comparatively too complicated to be worth the hassle, and since you use Chrome, I suppose you have access to an internet connection. You can boot from the old disk (installed in a HD case compatible with one of your Mac's expansion ports) for syncing.
iPhoto Library is in