What am I doing wrong with my drains?

I dont know much about plumbing or even what system we have so youll have to excuse the vague description. We have an outdoor drain - made of concrete on concrete pavement at side of house and is a walled in rectangle shape. It seems we have a pipe going into it from the kitchen sink and a pipe from the washing machine and dishwasher. This drain keeps overflowing. Someone suggested the system needed rodding as the blockage may be unseen. The landlord seemed to do stuff just around the drain. We have no idea what they do but when I mentioned rodding he said thats what theyve been doing (4 times) and it costs 200 pound a time and it must be because we put food down there. Since this I have made every effort to be strict with housemates - we wipe plates with paper towels and also have a plug sieve. But its overflowed again. I emptied it today with a plastic bag on my hand. The problem seems to be gray sludge with white flecks that smells like rotting poo. Is it us or the drains?