My lights / or water / or phone has been turned off.

Hola, Elisa, you appear to have it right. You could say, "they turned off the electricity because I had not paid the bill" or "they cut off the electricity ... " or "they are threatening to turn off the electricity ..." (in place of "electricity" you can put "water" or "telephone service"). People use the term "outage" when there is a natural disaster or there is not enough electricity for everyone. Then you could say there is an "electricity outage in my neighborhood".

Hola, Para decir eso usas "Cut off the service", por ejemplo "They cut off my electricity service because I didn't pay the bill". Usarías "outage of service" cuando es un problema causado por un desastre natural, o cuando falló la empresa del servicio. Un ejemplo de la situación es cuando se te corta la luz porque hubo un terremoto el día previo. Dirías "There was an outage of service due to an earthquake took place yesterday". No se si me expliqué bien

They have terminated our electricity service due to non payment of electricity bill,. There was outrage of current due to earthquake yesterday. If you want to practice English follow and message me

Muchas gracias