Which sentence does not contain any punctuation errors?
a. my brothers cleaned up washed dishes and put the leftovers in the refrigerator.
b. my brothers cleaned up, washed dishes, and put the leftovers in the refrigerator.
c. my brothers cleaned up, washed dishes, and, put the leftovers in the refrigerator.
d. my brothers cleaned up, washed dishes and put the leftovers in the refrigerator.

Both B and D are correct forms - the last comma is optional.
I would use probably use a comma  here because the brothers' tasks are so diverse. However, I am not forced to use it - it is optional.

I would not use it here:
I am considering a HP, Dell and Lenovo as possibilities for my next computer.
(Because they are not diverse - they are all brands of computers). 

What's wrong with A - It sound as if your brothers dropped the dishes as they took them out of the dishwasher and had to clean up all those broken washed dishes.
C is wrong because of the unecessary common after the "and".