Since elementals have languages that can be learned and spoken by anyone, are you able to speak freely with any language you know to fulfill the conditions of spell casting and communication?
If an elemental can normally speak, this GM would allow a creature that assumes that elemental's form to speak also
The description of the polymorph subschool, in part, says
When you cast a polymorph spell that changes you into a creature of the animal, dragon, elemental, magical beast, plant, or vermin type, all of your gear melds into your body. Items that provide constant bonuses and do not need to be activated continue to function while melded in this way (with the exception of armor and shield bonuses, which cease to function). Items that require activation cannot be used while you maintain that form. While in such a form, you cannot cast any spells that require material components (unless you have the Eschew Materials or Natural Spell feat), and can only cast spells with somatic or verbal components if the form you choose has the capability to make such movements or speak, such as a dragon.
Many creatures of the elemental type can speak naturally, so this GM would rule that if a creature assumes an elemental form that has a language, the creature can speak normally in that assumed form. (This also seems to jibe with the description of the feat Wild Speech.)
However, "the GM is the final arbiter of what abilities depend on form and are lost when a new form is assumed," so a GM may rule that a particular elemental form lacks "the capability to make such movements" that are appropriate to casting spells. That seems a little rough to this GM and player, though, as that pretty much bars a fair segment of extraplanar creatures from ever being spell casters.