I have no idea how each airline is organized but I had some insight on one as I was visiting a workshop for handicapped:

One of the main job these handicapped people had to do was cleaning and repairing headphones, blankets, pillows for an airline.

These were gathered together at the end of the flight and brought to that facility. Each headphone was being tested , than cleaned with a special product and packed in little plastic bags.

The blankets were being cleaned in big washers, but I think it was some type of dry cleaning, checked for damages and also packed in plastic bags and returned to the airline.

The planes themselves are cleaned somewhat summarily after every flight but as far as I could find out, a thorough cleanup happens only during the plane's big overhaul and this is not very often... I remember some AA planes on which one could have guessed a month's menu by studying the smearings and crumbs.