The wings are mostly a Pagan artistic influence (mostly from my girl Nike), the Bible mentions only cheruvims and seraphims as having wings. Otherwise, angels always appeared as ordinary men (literally men, never women) – f.e. in the Lot story about Sodom and Gomorrah (when Lot offered his virgin daughters to be raped by the townsfolk, instead of the angels), in the story of Abraham dining with God and receiving the promise etc etc. Here’s Cracked’s nice little take on it.
As for the question on why incorporeal creatures would take a human form (to appear in front of a bunch of Bronze Age savages, which is an answer in itself, hence this, this, this and this) – well, you could also take “God created us in His own image” literally. But, yeah, it’s usually just to blend in and if alien worlds exist, they’d probably accommodate to them as well.