OpenDNS is update by SSL/TLS (https) with the following URL:

https://[USERNAME]:[PASSWORD]@updates.opendns.com/nic/update?hostname=[DOMAIN]

OpenWRT doesn't ship with curl used to update HTTPS sources, so we need to install that.

root@OpenWrt:~# opkg update
root@OpenWrt:~# opkg install curl

Now we need to download the latest Certificate Authority bundle. Such a bundle is in the PEM format and can be downloaded from http://curl.haxx.se/ca/cacert.pem.

root@OpenWrt:~# mkdir -p /etc/ssl/certs/
root@OpenWrt:~# wget -P /etc/ssl/certs/ http://curl.haxx.se/ca/cacert.pem

More in depth information can be obtain at the OpenWRT wiki page for DDNS.