Does entering a pornographic website—with the intention of testing a program to block pornographic websites—count as a breach of the oath sworn by the questioner not to enter pornographic websites, and is expiation obligatory upon him?

There is no breaking of the oath (hanath) in what occurred to you regarding seeing certain websites when testing the mentioned program to block them, because there was no intention to view the website. Rather, the intention was to test the program's ability to block it. The intention of the swearer specifies and restricts his oath, as do custom and the context of the oath. These matters are all present in your oath, so no expiation is required of you.