This is the result of metanalysis, a phenomenon in a English (and Dutch!) where words beginning with N go from, eg. "a numble pie" to "an 'umble pie" or in this case, "a noodle" to "an oodle" to "oodles".
Now, obviously trying to count the number of noodles in a bowl thereof is a frustrating and pointless task, and from this we see the meaning of "oodles" as "too many too count". So what is an oodle? It's just one thing, probably; countable, finite, but long and wibbley.