StrikeBase Calendar lets you invite users to an event and keeps track of their responses.
To invite users while creating a new event check the Guests option to the left of the Create Event button.
In the Guests section you can type in the names of the guests or you can click on the Add Guests icon to open up the People popup from where you can select the users.
To invite users to an existing event click on the Manage Guests icon in the event details popup.
Note: You can only invite guests to an event if you are the creator or you have the required permissions.