Outside Odd Sudoku (Daily Sudoku League #97)

Outside Odd Sudoku recently appeared in the German Sudoku Championship 2015. This Sudoku type was new to me and I created this puzzle to get familiar with this Sudoku type.
The Sudoku Mahabharat Neighbours round has started. Please participate in this and let me know your feedback regarding this test, so that I can improve any shortcomings for future tests.

This Outside Odd Sudoku is my 97th contribution to The League of Extraordinary Ladies and Gentlemen. Can you solve this Outside Odd Sudoku puzzle?

Rules of Outside Odd Sudoku

Classic Sudoku Rules apply. Additionally, clues outside the grid indicate the number of odd digits in the first three cells.