For wolves, perhaps cold, hunger, or civilisation? Depending on the type of animal, they might be susceptible to taming or to a certain type of predator. Some animals also have a weakness for a certain type of plant or herb (e.g. catnip).
I understand the principle of opposition but I still don't really see a watery being being much harmed by earth - or at least most types of earth. Throwing a stone in a pond doesn't really damage it... I'd suggest something like cold (to freeze the water) or something fine-grained or powdery (e.g. sand) to absorb it. Also fire, but less effective since water generally "wins" over fire and it takes a prolonged effort to boil water away.
Don't really see this... The best thing you can do against something insubstantial is to try and blow it away/apart. Thus the best defence against air would be... air.
Presumably this would be something like a skeleton, a ghoul, or a magic human. Iron is good for wounding, shackling, or imprisoning human bodies. If a skeleton, stone is good for smashing. Also Mentem, since the mind rules the body, and humans are susceptible to being ruled or enslaved.
Trees are susceptible to fire, lightning, and being felled with iron axes.
Yes, this is the elemental opposition that makes the most sense! As per water, something powdery could also be used to smother a fire.
Illusion is countered by perception (Intellego). The weakness of such a being would be being able to see its true nature.
Presumably some kind of ghost? Such beings are susceptible to all mortal weaknesses: temptation, deception, flattery(pride)... In other words, Mentem would be countered by Mentem.
Something made of earth or stone is unlikely to be bothered by a bit of wind! Stone can be countered by iron tools or ice. Soil can be broken by tree roots or heat, or washed away by water.
The trickiest one! Magic is generally countered by magic... The power of the Divine is also an obvious weakness.