I have a massive Catalpa (sp) tree in my front yard. The trunk is about 4 feet in diameter at ground level. About 10 feet up the trunk, there is an oblong hole that's about 10" tall by 4" wide. I think squirrels are living in there. While I don't want to harm the squirrels, I don't want to lose the tree. Should I repair the hole and if so with what, or should I leave it alone. The hole is not at a fork.

Let it alone. You will only due more damage and cause rot, to understand any tree read this from Dr. Alex Shigo:
http://home.ccil.org/~treeman/shigo/index.html
It tells how a tree defends itself by isolating the injury.

More on Shigo:
Shigo - Google Search

K