Does anyone know where this use comes from? Is it a corruption of 'of'?

So far as I can work out from other contexts, the "meaning" of 'off' in this case is a reference to the number that are taken "off the machine" after production. It also has the connotation of "off the stores shelf".

The necessity to use this construction lies in the probability that the object being "taken off" is identified by a numerical tag - size, dimensions, parts number or w.h.y, so it is essential to separate the quantity of the good from its numerical tag.

The other (and increaingly popular) way of differentiating in this way is to use "No.", as in "4 No. 30mm x 1550mm strips" if you actually want four of the strips of whatever.