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Mysterious Stranger |
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Like any polymorph spell you only gain the abilities listed in the spell. Since elemental body does not list any of the abilities an invisible stalker has you gain none of those abilities including their invisibility.
I suggest you look up the rules for polymorph spells in the core rule book under the Transmutation school.
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Rule of thumb for Polymorph spells/abilities: If an ability isn't specifically listed in the spell text, you don't get it.
The only exceptions for this are the abilities specifically listed in the Polymorph rules.
Polymorph abilities have a long history of being completely broken (the 'D' in 'CoDzilla' is for a wildshaped Druid) and inherently impossible to balance if able to grab nearly any ability*, so they are now highly restricted in what they give.
*Polymorph abilities tended to get more powerful as more creatures were added to the game for the PCs to fight, as that just gave the PCs more (and often better) form options: In D&D3.0, you could grab a nearly permanent Haste bonus (back when haste meant two spells per round) with the right feat selection (because they accidentally gave one monster a permanent Haste effect as an extraordinary ability), and even I played a character who abused Alter Self to get the Troglodyte's +6 natural armor bonus...