Janna's Eye of the Storm provides a shield that absorbs damage and gives a boost to AD. Suppose Janna shields an ally with a hexdrinker; would Janna's shield have to be destroyed before hexdrinker would be triggered? If Lux and Janna both shielded an ally, which shield would be consumed first?
In League of Legends, shields come as additional health. That is to say, your health is increased by the shield value. With regard to this remark, the order has no interest for the Hexdrinker. If your health + shield value drops below 30%, the Hexdrinker shield is cast.
As far as other cases are concerned, there seem to be multiple debates over the internet and the LoL forums. The most convincing answer I found is that shields are consumed in a "First Cast, First Depleted" (FCFD) order. As the shields stack (you can see that with the grey bar when multiple shields are on you), it would make sense to consume the first shield first to maximise the absorbed damage (as the second shield should last longer in term of duration). Nevertheless, it could happen that shield order and duration are not the same (Janna's shield followed by Blitzcrank's shield for example). In that case, it would be more effective to consume Janna's shield first, but there is no mention of another behaviour anywhere.
As a conclusion, "FCFD" order is the most probable answer, "earlier expiration depletes first" could be another approach but is less probable (harder to program). Finally "Last Cast, First Depleted" could be the third way to do it, but is also less probable due to the unoptimised behaviour that will then occur. Another remark, multiple casts of the Locket of the Iron Solari shield have a special rule (they do not stack and the effect is reduced).