Use a VPN Service.
VPNs re-route your data through another server, masking your network activities from security software like OpenDNS.
Use a Free Proxy Service.
A proxy service can re-route your traffic in a similar way that a VPN will, but lacks some other privacy features. If your only purpose is to bypass OpenDNS, then a free proxy will accomplish that.
Use TOR Browser
Download and Install TOR browser on a USB drive. TOR is a browser that has a built-in proxy that will allow you to visit any website you want, although it may load slower than any other browser would.
If your phone is capable of it, you can use its cellular data connection as a Wi-Fi network and circumvent the network restrictions.
What is OpenDNS?
OpenDNS is a company that offers simple Internet navigation and security solutions for families, schools, government agencies, and enterprises of all kinds. It is most known for blocking adult content.
Is OpenDNS safe?
OpenDNS is considered safe to use and does not collect any more data than an antivirus would, which also has the same features built-in.