Discontinue Your Alerts
If you want to discontinue your Google Calendar alerts, you will need to start by pulling up your Google Calendar. Just go into your account and click on the calendar tab to get onto the general screen for it. Your next step will be to look in the top right corner. You should see a tab labeled settings. Click on it, and then look for calendar settings in the menu. Click on this to pull up the settings page.
Once you're inside the settings page, you'll need to do a little bit more work. This first page for calendar settings just covers the general information. You can set up a few neat options here. Beyond the basics of setting up your calendar's format, you can also pick your default method for handling invitations (automatically accept, add but don't accept or don't add until you accept), or even set your usual work hours to warn people who send you invitations that you won't be able to honor.
While this is all well and good, the setting for turning off Google notifications is partially hidden away. Look in the top row for a few more tabs. Once again, you'll need to select the tab marked calendars. Pull this up to see the selection of all of your current calendars. Along the row for each calendar, you should see a highlighted link marked notifications. Click on this to bring up the full page for notifications for that calendar.
If you want to shut off all of the notifications, just uncheck all of the boxes. Otherwise, pick the ones that you want and then save the settings. Note that you'll need to do this for every calendar that you've set up, and it may actually take a day or so for the changes to actually take place. You should be free of the alerts soon though.