The Sheik, Durga and Ali families share the Welbedacht East home.
Afzal Sheik, 47, who lives with his parents, wife, three daughters and two grandchildren, said the families live in poor conditions, surviving on two pension grants, child support and odd plumbing jobs.
Sheik said contractors were flushing out drains in another area when they noticed water pouring out from their stormwater drain on Thursday. The contractors said nothing could be done because the pipelines were damaged.
A storm on Saturday night caused the pipeline to burst, causing damage to the house when the water surged inside. A one-month-old baby nearly floated away on a mattress, Sheik said.
He said the family got out safely but were back to sleeping in the muddy house.
Sheik said neighbours were cooking for them and when it rained on Tuesday they went to their neighbours for shelter.
Their children did not go to school because their clothing was washed away or is buried under the mud.
Ward councillor Anoop Rampersad said he had liaised with the eThekwini Municipality and understood that litter stuck in the pipeline had caused the burst.
He said the pipeline runs under Sheik's house.
Jet cleaners were used to push the rubbish out, but boulders were found further down the pipeline.
In order for it to be fixed, the house would have to be destroyed, said Rampersad.