VoIP is a big subject and a few searches on Google should get you plenty of articles to read up on.
Basically, Skype is one option as mentioned by other posters, however (again as mentioned), Fring is a better choice as it allows you to call on Skype via your internet connection (the Skype client doesn't).
If the E71 is anything like the N95 family of phones, i.e. it has an Internet Telephone application built-in, this is even better as it can get you out of the confines of Skype and into the world of SIP. Again a few Google searches should explain to you what this is. Check out sites like callcentric.com, voipfone.co.uk, sipgate.co.uk to get an idea. You can set up any of these services on your phone's Internet Telephone options, and by adding some credit to your account with the SIP service, you will be able to make VoIP phone calls on your Nokia through your WiFi connection at the SIP provider's cheap rates.
When connecting your phone to your home broadband via WiFi, this has absolutely nothing to do with O2 and with your mobile phone account/service with O2.
For the record, VoIP on Nokia phones (and Fring) will work not only via WiFi but also over a 3G connection. However this is against O2's T&Cs, as you pointed out.
Nevertheless, that part of the T&Cs is there to prevent abuse, rather than every single instance of VoIP or streaming use