It is possible to manage an unmanaged VPS server with Odoo after installation, but it may require some technical knowledge and experience. There are a number of tasks that you may need to perform to keep the server running smoothly, such as applying updates and security patches, monitoring the server's performance and logs, and managing backups.

To ensure that the server is stable after the Odoo installation, you should carefully follow the installation instructions provided by the hosting provider and the Odoo documentation. You may also want to consider using a pre-configured Odoo installation package, such as the one provided by the hosting provider, to simplify the process.

As for backing up the server, it is generally recommended to create regular backups of your Odoo database and files, in case something goes wrong. This can typically be done using the built-in backup and restore tools in Odoo, or using a third-party backup solution. Again, it may be helpful to consult the documentation and support resources provided by the hosting provider and Odoo for guidance on how to create and manage backups.