What can cause a 1993 Honda accord to lose all of its oil in a few minutes?

You may of blown the seal out of the balancer shaft under the timing belt cover. The balancer shaft keeps the engine from vibrating, especially at an idle (like a harley.). This could cause a sudden and voracious oil leak like you described. The bummer is that it is under the timing belt cover, and its just like changing the timing belt to fix it. The oil will run down the engine, and leak out around the pan gasket area, while being hidden on the way down by the belt cover. Good luck.