These words are related and doing one often implies doing the others at the same time, but they have slightly different meanings.
Hosting is when you provide something using your personal resources. It is possible to "host" an event without being in charge of it, or responsible for its organization, by simply providing the space and other amenities for it. Of course it's also very common for the host to be the one in charge of the event, but it's important to note that hosting something does not imply ownership of it.
Holding an event implies ownership and responsibility for its occurrence, but does not necessarily imply they are providing the venue for it. Holding is essentially the counterpart of hosting, they often go hand in hand, but they can be handled by separate people or groups. You would use this to describe who is in charge of the event, but not necessarily where it is being held.
Organizing an event implies leadership and responsibility for making it happen, but not necessarily ownership of it. It is possible to organize something on behalf of others, essentially doing the grunt work of planning, scheduling, provisioning, and so on, without having a personal stake in its outcome or a personal connection to the event's topic or goal. Of course, as with the other two, it's possible to do all the organizing for the events you host and hold yourself.