Your first sentence is wrong no matter what style of writing you use. A comma before the 'and' is very helpful in a few odd cases. The extra comma also looks nicer in my opinion. However, many publishers hate the waste of ink for the extra comma. Thus normal printed text will not include these commas.
Try the following sentence both ways:
(1) The old toy box contains porcelain dolls, rag dolls, and plastic dolls; blue, red, and green trucks; and blue, yellow, and white crayons.
(2) The old toy box contains porcelain dolls, rag dolls and plastic dolls; blue, red and green trucks and blue, yellow and white crayons.
I know they are run-on sentences; however, both sentences use approved punctuation. In my opinion, the first sentence is much easier to follow. The extra comma and semicolon make the list of lists much more legible.
Edit: I corrected a spelling error.