Hello, I'd like you to help me.
Why and what is the difference in order of adjectives between Cambridge and Oxford? Oxford: opinion, size, age, shape,...
Cambridge: opinion, size, shape, age,...
What does this mean? Can we do bothways or what? I am baffled, I admit.

I didn't even know that Cambridge and Oxford didn't agree on this! In any case you don't often have age and shape in the same sentence, but as a native speaker I would say something like this:

1. An expensive modern German car.
2. A funny green cotton cap.

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Here is a table which might help you:

How much/many?	What’s it like?	How big?	What shape?	How old?	What colour?	What’s the pattern?	Where’s it from?	What’s it made of?	What is it?
a/an	beautiful	little	square	old	pale red	check	French	silk	scarf
one	nice	small	round	new	light yellow	striped	English	cotton	blouse
three	ugly	medium-size	oval	modern	bright green	plain	Japanese	wooden	desk
some	clean	average-sized	rectangular	antique	dark blue	flowered	German	leather	car
a few	dirty	large	pointed	19th century	brown	spotted	Italian	gold	house
several	cheap	big	triangular	1930s	black		Roman	metal	box
a lot of	expensive				white		Parisian	paper