I've heard SODAs are hard to get, but have no personal
experience.

Not at all!
SODA aren't hard to get. There is a guideline that a person must complete to
pass the SODA. For example, color-blinded person must pass light-gun test.
There are guidelines for various condition such as deafness, amputed leg or
arm, and many others. I have no idea about stabismus condition. Assuming
that it does not affect your driving ability, it is safe to assume that you
will pass SODA if they ask you to take. You probably will perform few tasks
such as turning, climbing, possibly under hood work, etc. Nothing that will
make you sweat.
Toks Desalu