I just installed an antenna and tried OTA programming on my Roku TV. In addition to the dozens of familiar OTA channels, hundreds of "Roku Streaming" channels appear and are accessible — despite my cable being disconnected. How is this possible?
Your title says "no Internet" but your description says "my cable is disconnected". Those aren't the same thing unless you're talking about a physical cable. It should be impossible to get any stream of any kind without Internet service, but that has nothing to do with a cable TV package. I would guess your TV is connected to someone's Internet service. What does it show under Settings->Network->About?
I will check to see if some Wi-Fi connection exists.