When to Use "OFF" and "ON"?


if it's better to contribute my thoughts "off" the topic or stay focused "on" the discussion at hand.

Hello! Thank you for your question.
In this instance, 'off' could never be used. The word 'off' is used to indicate separation or disconnection: 'He drove off the edge of the cliff'.
In your first phrase however, you could use 'of' which is used to indicate a relationship between something - 'my thoughts of the topic'. That would be acceptable if you were referring to your thoughts about the topic that has been chosen in relation to other topics.
It would also be acceptable to say, 'my thoughts on the topic', if you were referring to the details of the topic.
In your second phrase, it's only possible to use 'on' - 'stay focused on the discussion at hand'.
I hope that this helps answer your question.