You can use a cron job to call the Salesforce Data Loader from the command line and load the data from the files. Each object will require a separate job as the Data Loader only supports a single object being loaded at a time, this also means that the sequence of the jobs needs to take into account any dependencies in the data between the objects.
The data that you want to load would need to be stored in a folder that is accessible by the user that is used to run the Salesforce data loader.
Data Loader command line interface
Data Loader guide
It is good practice to have a separate user account used for this with just the permissions needed for the objects in integration not a System Administrator account as that would be able to modify user permissions.
Alternatively Data Loader can be used manually by a user with permissions on the objects (if this includes custom objects then they are likely to need Modify All Data and API permissions)