Stir together soda and 1 1/2 tablespoons water until dissolved.
Beat shortening at medium speed with an electric mixer until creamy. Gradually add sugars, beating until fluffy.
Add soda mixture, eggs, and next 3 ingredients; beat until blended.
Combine flour, oats, and baking powder. Gradually add to shortening mixture, beating until blended. Drop by rounded tablespoonfuls onto lightly greased baking sheets.
Bake cookies at 350 for 10 to 12 minutes.
Remove to wire racks to cool.
Stir together powdered sugar and orange juice; drizzle over cookies.