You can only have one of these active effects at a time.
The wild form "works like" the beast form I spell, except as indicated here.
Beast form and Elemental body are transmutations (polymorphs), so the rules of polymorphs are applied. And, of course, the rule about the polymorph that worried him (which also refers to Wild Form):
You can only be affected by one polymorph spell at a time. If a new polymorph spell is cast (or if it activates a polymorph effect, such as the wild form), you can decide whether or not to allow it to affect it, taking the place of the old spell. In addition, other spells that change size have no effect on you while you are under the effects of a polymorph spell.