How do house flies affect people plants and animals?

House flies generally clean up things they can eat, or lay their eggs in/on them so their larvae can eat them if they have the peace needed to do so quietly. So they'll eat your food, and eat/lay eggs on garbage, dog poo etc. They will not leave terrible bacteria while doing so - ever seen a fly rub its 'hands'? That's cleaning behaviour, just like a washing cat. They do it all the time, and they clean their entire body. A house fly is as dirty as your house, and even then only until it cleans itself. ^^ So generally they are completely harmless, if a bit annoying due to the buzzing.

They have no real influence on plants as they don't eat them or lay their eggs on them.