Here's why:
* Quaint: charmingly old-fashioned or unusual.
* Real: authentic, genuine, or true. (This one is a bit of a stretch, but it can sometimes be used to mean "peculiar" in a playful way.)
* Queer: strange or odd.
* Odd: strange or unusual.
Peculiar encompasses the sense of being different, unusual, and sometimes slightly strange that all these words share.