In which region, of which state, would you find a religious sect that refer to themselves as the Old Order?

You refer to the Old Order Amish.

They live in various states in the US, most notably in Pennsylvania (especially Lancaster County), Indiana and Ohio. Land prices, especially in Pennsylvania, have become very high, so they are moving to places in the American west, like Montana.

Some Old Order Amish also live in Canada-in Ontario.

There are Old Order Amish communities in at least 20 US states.

http://pittsburgh.about.com/cs/pennsylvania/a/amis...

http://www.religioustolerance.org/amish.htm

http://en.wikipedia.org/wiki/Amish

these are amish and mennonites. though found in many parts of canada and the us. a large number are in wellington county, ontario canada

a nursing home in florida