When to use override and overwrite

Solution 1:

"Override" is the cancellation of some previous action or decision. "Overwrite" specifically refers to something being written over something previously written. In other words, actions and decisions are overriden. Information is overwritten. Furthermore it is overwritten with new information.

Therefore in your example, overwrite is appropriate:

The administrator has the right to overwrite the user time slot for the venue A inside the online system.

A similar example where override would be appropriate is:

The administrator has the right to override all venue decisions made in the online system.

edit:

In some contexts, override could be correct. Specifically, consider the following scenario. Say that the meeting is already scheduled to take place in room 117. Then, another employee changes this location to room 119. In this case, the administrator would override this decision, rolling the location back to room 117.

However, it is equally correct to say that the location was overwritten to room 117, and there is nothing in the original sentence to imply that this scenario is the case. For that reason, I would say that "overwrite" is the best word choice.

Solution 2:

To override is to take over, or exercise power above the normal level regardless of common rules. To overwrite is to replace.

In this case, I would say override, as the administrator is using their power to 'break the system'. That said, it still largely depends on the context around it, so if you gave some more information I would be able to help some more.