Turning off the default calendar program almost certainly requires root, and even then I'd approach with care (i.e. make sure nothing else depends on it). But you should be able to turn off notifications from the default calendar program.
In the actual default Android calendar you go into settings, select "set alerts and notifications", and turn the notifications off there. Unless you are using a custom ROM it will be the Sense calendar you have, so the setting may be somewhere else - it's a long time since I used Sense, so I don't remember - but there should be an equivalent setting in there somewhere.