The Aqueos Orb spell description says that it works like dispell magic on magic fires. It´s not directly RAW but I´d say you can apply this to fire elementals - so at least summoned fire elementals can be dispelled by it
As for other elementals, there seems to be nothing in the RAW, however, only a bad GM would say "there´s no rule, I don´t know what to do", just do what seems logical - letting the air elemental avoid the entangling, let the water elemental be "entangled" but since it´s damn fast in water, it can escape quite easily, let the earth elemental be fully affected and let the fire elemental take additional damage (but no entangling for him) or something like that.
Rules have to be a help, not a hindrance.
What happens to elementals that get entangled and damaged in the Aqueous Orb spell?
Fire and earth elementals can't get in water
Air can't move in water
Water elementals doesn't sound like it would take damage or get entangled by it.Just curious.
Actually air elemental description specificially says that it can move in water but due to lack of swim speed and 0 ranks in Swim skill loses much if its maneuverability. Earth elementals are probably to dense to swim and thus are limited to walking on the bottom of any water terrain feature, probably at half speed as it would be difficult terrain for them. Only Fire elementals are specifically incapable of entering water. However, looking at the description of aqueous orb I would say that its effects are enough. Maybe make Fire elemental vulnerable to nonlethal damage from that particular spell and give it penalty to saving throw to escape orb - as the water becomes more resilient barrier to its attempts to leave entanglement. I would also make Water elementals immune to engulfment effect.
All other elementals interact with aqueous orb as described.