Learn English – alight vs drop me off vs drop me at

The usual way is to say:

He dropped me off at the airport.

You would not use drop unless something was actually dropped.

airport drop off would be more of a noun usage:

After the airport drop off he went to the ticket counter.

The phrasal verb "come off" is listed to mean to take place/happen not only in the Free Dictionary but also in other dictionaries (Oxford, Macmillan, Cambridge, etc.) with examples similar to those mentioned by the PO.

Accordingly, I don't find any difference in meaning of "come off and take place" except that (per these dictionaries) "come off" is informal and "take place" is common both in spoken and written English. Being a non-native speaker, I have no idea of how much the phrase come off is common or popular with native speakers.

So it's correct to say that "Is the meeting going to take place or come off today?" Likewise, they are interchangeable in the examples mentioned in the question. However, I don't think it is proper to use come off for something that happens/take place by chance/accident or without being planned such as a car accident, a plane crash, etc.