The seven are
January, March, May, July, August, October, and December
The least is
We’re the Greatest of our siblings
Always best since days of yore
Our Least brother’s always nibbling
Now and then he gets one more
Greatest since they have 31 days. February has the least days with 28, but sometimes has 29 on a leap year.
First and last are far yet near
Fourth and fifth together chained
One through four are strange or queer
Five, six, seven are level planes
January and December are 1 and 12, but January is one month from December. Edit from the comment: Four and five, July and August, are the seventh and eight months, so they're chained together. One through four are the first, third, fifth, and seventh months, which are odd. Perhaps August, October, and december are equally separated by two months, so they're level planes; or they're all even (level) at eight, ten, and twelve.
Flavors are our favorite number
It describes our special quirk
With these clues you’re now encumbered
Knuckle down and get to work!
31 flavors is a reference to Baskin Robins' flavors.