I mailed in my payment for my state taxes that I owed. How can I check to see if that payment was recieved?

I recommend you check your bank activity and see of the check has cleared the bank.  If you prefer, you can call your state's department of revenue.

It was a money order I mailed since they don't accept personal checks and they don't answer their phone. Is there somewhere online I can look?

It is very difficult to trace a money order. As DavidD66 mentioned, you can call your state department of revenue to verify if your tax return has been received or processed. You may be able to do this online but please understand that all states may not have an online feature that tracks the progress or receipt of your return like the IRS.

Check out your state in the link below to see if that is an option for you.

How do I contact my state Department of Revenue?