Probably not from the ADB Backup (to my experience, SMS are not backed up with that) – but from the Nandroid it should be possible. You'd need to extract that, find the messages database, and then you can access it using some SQLite client (depending on the OS your POC runs). The Nandroid should also hold all other personal data, but might lack your "internal SD card" data – which might be part of the ADB backup, depending on how that was run.
Some types of Nandroid do file-system images. But the default nowadays is a Tarball, i.e. a simple archive containing the directory structure and the files within. That's also the case with yours, as you confirmed – so you can open
data.ext4.tar (which holds the contents of your
/data partition) in e.g. WinRAR/WinZIP and see if it lists directory structures. I expect it does. You're after something in
data/com.android.providers.telephony/*, where you should find a file named
mmssms.db or similar (I don't remember the correct path and file name by heart). That's where your messages are in.
For completeness: would your Nandroid be an image file, you can e.g. use Testdisk to browse and extract contents from it.
As for other "personal data", depends what you're after. See our data-recovery tag for further hints.