Here is the documentation for the required Network Ports. For ILLiad, connecting to the SQL server uses ports 1433 and 1344.
If you want to use the non-standard 1344, be sure to add it to the SQL Alias Manager after the server, without spaces. For example: yourserver.illiad.oclc.org,1344
For OCLC Hosted ILLiad institutions, editing web pages and uploading patron loads via SFTP is done via port 222.