Also I usually had sudo privileges, but when trying to use the sudo command in PuTTY, it said that is not included in the sudoers file. Any help would be much appreciated.
This command would have removed your other privileges, including sudo: sudo usermod -G root orin
This command would add you to groups root and orin (if it exists), but would have erased all other groups (including sudo): sudo usermod -G root orin
You were already in the sudo group if you could run any of those commands, but now you have no sudo ability. Unless you have a second admin user you’ll need to flash again. There is a minor possibility of editing the SD card on another Linux PC if you are using this as an SD card, but it may not be worth the learning curve.
In terms of what you wanted to accomplish, was it just use of root without a password? If so, then this is the wrong method. One thing you could have done is to unlock the actual root account. Another is to use sudo once to log in either directly as root or in a root shell (almost equivalent):
sudo -s (root shell)
sudo - (actual root login)
In order to fix the issue on the Nano you would need to have an sudo account. On a Linux host PC there might be ways, but flashing is probably easier. However, it would be easy to back up some content from the SD card if you have something valuable. Or simply use a different SD card for installing. If this is an eMMC model, then you’d require cloning to back up or save anything.
If you want information on unlocking the root account instead of using sudo, then just ask here. One can unlock root for specific cases too; the most useful is to allow root login via ssh if keys are used, but to deny local login (already the default) and to deny password-based ssh login (already denies this). Key based access is much safer, and also make development quite easy.