How do you pronounce on the twenty secondth day of october?

Here, the ordinal is not a fraction, so it should be just "twenty-second day."

* You may encounter the use of the informal Word secondth, such as in the fraction

3/22 = three twenty-secondths.

But note that the convention for numbers ending in one, two, or three use the simple ordinal, e.g.

1/21 = one twenty-first

1/22 = one twenty-second

1/23 = one twenty-third