Great Old One's Tentacles and Enemies Explode Mechanics.

When combined together. Does the reflected impale damage and the explosion damage stack together? Or does the explode takes priority first and does not allow for a impale reflect to happen?

Explode effect happens simultaneously. If you have a "explode for 25% life as PhysDamage" and "explode for 10% life as chaosDamage", the corpse will cause 2 explosion for the aforementioned type and magnitude.

I'd say on kill effects (like, say, Flask charges gain on kill) happens at the same time of explosions, which are on kill effects as well. I'd expect Old One and Explodies to work at the same time when killing an Impaled enemy: you will deal physical damage (as reflected damage) to nearby enemies AND deal the explody damage.
It's not like Old One needs a corpse in order to work, like Porcupines