5/16 inch thick strips - width 2 or 2-1/4 - for older parts of home
5/16 thick unfinished flooring is hard to find.
We located 2 lumber mills in the bay area that will sell 5/16 strips :
Southern Lumber @ $4.50/sq ft! And Minton's lumber @ $.87/linear foot!

I assume you don't need much, just to repair some damaged pieces?
Suggest buying standard 3/4" oak strip, plane it down to 3/8", then use
a table belt sander to get it to exactly match the thickness of your older
5/16" (which may only be 1/4" if it's been sanded and refinished over the
years).

2. Do any of you pros on this board know where we can buy Unfinished
Red Oak Solid Wood flooring for reasonable prices? We prefer Select
grade, if at all there is a choice.

Home Depot sells NOFMA-certified select red oak (3/4"x2-1/4") for
about $2.59/sf, #1 common for $2.29/sf (less if you have a coupon
or if its on sale or if you buy enough to do a house; I got 20% off).
I don't understand Ed's comment about quality - each strip has the
NOFMA stamp on the bottom, and is the best stuff I've every used -
their select had not one defect in it, and the #1 common was almost
free of defects (about one per bundle).
- Rod