The Maiar are Ainur just like the Valar - they don't need to be physically embodied in the manner of men and elves, and often aren't until they find need to.
The Istari did *not* look like the old men they were disguised as when sent to Middle-earth. It is said that Olorin often walked among the elves unnoticed, hinting that he often took on the elf look when he visted them.
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...take counsel with thyself, and remember who and what thou art.
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