Greasy spoon italian in Berkeley?
You might try Lo Coco's on Shattuck or their cousins' place LoCoCo's on Piedmont. Personally I don't think either is an exception to the rule that you should never order pasta at a pizzeria.
I think Giovanni's would be exactly the kind of place you're thinking of, if the food were good.
Bucci's is sort of a modern variation on heavy old-school Italian. Good food, unique style.