My answer remains HERE.
I will be available in the office (on) Wednesdays and Thursdays.
Is 'on' optional? Or it is better to have it in the sentence? Is it a case of British vs American English?
I would say that it's a matter of being formal & informal in using English Language. That is, In our day to day speach we can drop "on", or else it has to be there, gramatically speaking.