not true, you can use 1 ID for icloud and a different ID for store/facetime etc.
First what you need to do is isolate which device is not communicating with the cloud. You said you have several different devices, so pick one, enter a test event in your calendar and see if it shows up on the other devices. If it does, that device is fine. erase that test event and move on to the next product- create a test date and make sure it shows up on the other products calendars.
also go in to calendar app, in the upper left you will see a button that says "calendars" tap there and make sure all calendars are selected under icloud.
I would check that setting on each device.
Eventually afteradding a test date on each device you will find one or two that are not communicating that change with icloud. as long as the calendar settings are fine, go to settings>icloud>turn calendar OFF (yes keep a local copy) wait 10 seconds then turn it back on.
and this should be obvious but make sure calendars are ON in icloud settings for all devices
the below article says you can try a calendar refresh button as well in your calendar settings. by golly i never even knew that button was there. try that first! lol
http://support.apple.com/kb/TS3999 troubleshooting icloud calendar