Ok. The issue is that you are not syncing your Mac with your iCloud account (because you aren't running OS X 10.7.4 or higher), but it sounds like you are syncing your iPhone and iPad calendars with both iCloud and iTunes. When you sync the data with both iCloud and iTunes you end up with duplicates.
If you can't update your Mac you'll have to go to Settings>iCloud on your iPhone and iPad and turn Calendars to Off. When prompted, choose not to keep the data on your device (this will erase the calendar, which is fine because you will be syncing it back from your Mac using iTunes).
You mentioned that your Mac calendar was no longer syncing with your devices using iTunes, even though (I assume) you have selected to do so on the Info tab of your iTunes sync settings. To fix this, do the following:
- First back up your Mac calendar by opening iCal and going to File>Export>Calendar Archive. Save this file on your desktop in case anything goes wrong.
- Reset the SyncServices folder on your Mac as explained in this article: http://support.apple.com/kb/TS1627.
- Connect your iPhone to your Mac, check that you have selected to sync your calendar with iCal on the Info tab of your sync settings, then sync. If you get a Merge or Replace prompt for calendars, choose Merge.
- Confirm that your calendar is now on your iPhone. If so, repeat step 3 with your iPad.
If you are syncing your contacts with both iCloud and iTunes you will get the same problem: duplicate contacts. If so, do the same thing for your contacts (although you shouldn't need to reset the SyncServices folder again).