Are invoices say paid when they haven't been? this is throwing off our account balances. how can we fix it?

there are several reasons. 

Maybe you applied payment from another invoice to these, or amount of these invoices mistakenly zero or you created payment, and apply it to these invoices (I bet that banking account reconciliation will show it). 

The best if you can show your books to experienced QBO guy and he will resolve it in 2 minutes. 

Thanks for posting in the Community, @max22.

I agree with what Ed40 mentioned. In additional to that, the customer may have open credits, and you've enabled the option to automatically apply credits to open invoices. If that's the case, you can unlink the payment so the invoices will be open again.

Here's how:

1. In QuickBooks Online (QBO), go to the Sales menu at the left pane to get to the Invoices page. 
2. Click the invoice to open and tick the 1 payment made hyperlink below the PAID status.
3. Select the date, then remove the checkmark to the invoice to unlink the payment in the Receive Payment screen.
4. Hit Save and close to complete.

If you want to disable auto apply feature, here's how to do it:

1. Go to the Gear icon at the top right to get to the Accounts and Settings. 
2. Choose the Advanced menu at the left pane and click the Automation section.
3. Remove the checkmark in the Automatically apply credits box, then hit Save and Done.

Just in case, I'll add this article for future reference: Create and apply credit memos or delayed credits in QuickBooks Online.

Please let me know if you have any other issues or concerns by leaving a comment below. I'm more than willing to assist. Take care and enjoy the rest of the day!