Contact the hosting provider and tell them that CURL has stopped working and ask if you need to white-label some of the payment processors you are using so that you can post and receive data from CURL.
Since your web pages didn't change, it must be a server change that caused the issues. CURL is used to communicate with other web sites during checkout, since the error occurs with both paypal and eway, that is the most likely culprit. Sometimes hosting providers will install new security measures that might prevent your site from sending or receiving external data even though that is necessary for payment processing.