An event is something that happens. For example, writing this message is an event. An occasion is a more important event. For example, a meeting or date can be considered occasions.
An accident is an unintended event. For example, finding money on the ground or slipping in mid are accidents. Note that an accident isn't always a bad thing.
An incident, however, IS a bad thing. Slipping in mud, cutting my finger etc. It doesn't have to be accidental, but if it wasn't it implies someone else had ill intent.