The exact translation of this is actually a Latin word which you may recognise: factotum. For example, 'I'm a vegetable-peeler, porter, cleaner, dishwasher and general factotum'. It's quite an old-fashioned word, though, and I'd be surprised to hear a young person use it. Colloquially, you could use the phrase 'jack-of-all-trades' or 'man Friday/girl Friday' (this is a reference to Robinson Crusoe's all-purpose servant). Another colloquial phrase that comes to mind is the self-deprecating term 'general dogsbody', meaning that you are at everyone's beck and call for all sorts of menial jobs that need doing. More officially, these job descriptions could be something like 'general office assistant' or 'general kitchen assistant'. In the catering/hospitality trade, we also have the post of KP (kitchen porter) to describe the person who does most of the heavier and dirtier work behind the scenes - usually the lowest paid and hardest working person on the staff.

For the example you gave in a pizza place, that person would probably be called a kitchen porter. Roughly speaking the kitchen porter does the washing and drying up, prepares food for cooking (eg chops veg), takes care of food storage and things like that. In a more general way you can say something like "General Assistant" if you want it to sound official. Colloquially you can say "odd job's man" or (old-fashioned) "man of all work" normally for someone who is self employed and maybe they do a bit of painting/decorating, a bit of basic plumbing etc