What is an easy method of proving that a cryptographic oracle attack is possible?
We have a Padding Oracle if there is a different response from the server gives us an indication of the correctness of the pad (say if this needs proving). We can establish this by playing a game where we send badly padded cipher-text and random strings to the server, finally submitting some at random and seeing if we can get a non-negligible Advantage is guessing which one we sent. 

The problem is that this might be the "brute force" way. It's fairly easy to do if there is obvious data-leakage, but you have to check through a lot of side-channel attacks to rule out data-leakage to an efficient adversary. I sense you want a clever fast way to prove there is no data-leakage, which doesn't sound possible to me.