Turned off Cellular on iPhone, but service is still on?

My parents have the service turned on my phone and I'm no longer living with them, is there a way from my phone to turn off the service and use only Wi-Fi?

The Cellular you turned off concerns the data connection, not the phone's signal/service. Put it in Airplane Mode & turn back on Wi-Fi.

Call the company and cancel service. This is the only way you can stop service and not get charged.

you can take the SIM card out of the phone, this will stop service to the phone, but your service provider won't know you did that and will still charge you.